###################################################################### # # A 'most robust" Runge--Kutta (16:9(8)) pair # # These are approximate REAL coefficients # computed using MAPLE with 40 digits for # # a SIXTEEN-stage conventional pair methods of # orders p=8 and p=9, with dominant # stage order = 5, # # together with approximate coefficients # # for two interpolants of orders 8 and 9 # # which require 5 and 5 extra stages respectively. # (Companion files list COEFFICIENTS of the pair as exact # RADICALS, and 40-digit floating point approximations # otherwise.) # # This procedure is "most robust" in the sense that # all weights b_i are non-negative, the maximum # coefficient within b and A is not large, and # it has a propagating formula which almost minimizes # the 2-norm of the local truncation error as # # T10,2 ~ .0000003511 # # (Formulas with slightly different nodes c_i can # have a slightly smaller error norm perhaps # achieved by having a larger maximum coefficient.) # # Additional stages and interpolating weights allow # for the computation of an approximation at any # point of the domain of solution of order up to p. # These interpolants have continuous derivatives. # # Nodes c[17]=1, c[18] - c[21] were selected in an # attempt to minimize the maximum of the 2-norm of # the local truncation error over the interval [0,1] # for the interpolant of order 8, and this value is # # T_92 ~ .0000007987 # # This 2-norm has three local maximum values on [0,1]. # # The remaining five nodes were selected in an attempt # to minimize the maximum of the 2-norm of the local # truncation error on the interval [0,1] for the # interpolant of order 9, and this value is # # T_10,2 ~ .0000003511, # # the endpoint 2-norm error. This 2-norm is monotone # increasing on [0,1]. # # The formulas scanned for this optimal formula are # those developed in J.H. Verner, SIAM NA 1978, 772-790, # "Explicit Runge--Kutta methods with estimates of the # Local Truncation Error". It is conceivable that the # pairs in J.H. Verner, Applied Numerical Mathematics 22 # 1996, 345--357, "High-order explicit Runge--Kutta pairs # with low stage order", which also require 16 stages, # but solve the order conditions in a different way # may yield particular pairs of equivalant or more # efficiency. # ###################################################################### # # NODES # ----- c[1] = 0. c[2] = .40e-1 c[3] = .9648736013787361245235039379666356743708e-1 c[4] = .1447310402068104186785255906949953511556 c[5] = .576 c[6] = .2272326564618766017153738192188229509142 c[7] = .5407673435381233982846261807811770490858 c[8] = .64 c[9] = .48 c[10] = .6754e-1 c[11] = .25 c[12] = .6770920153543242682384311058159603931192 c[13] = .8115 c[14] = .906 c[15] = 1. c[16] = 1. # # ******************************************************** # NEW COUPLING COEFFICIENTS # --------------------- # for c[1] = 0. # # for c[2] = .40e-1 a[2,1] = .40e-1 # # for c[3] = .9648736013787361245235039379666356743708e-1 a[3,1] = -.198852731918229097650241511466089129345e-1 a[3,2] = .1163726333296965222173745449432724803716 # # for c[4] = .1447310402068104186785255906949953511556 a[4,1] = .3618276005170260466963139767374883778890e-1 a[4,2] = 0. a[4,3] = .1085482801551078140088941930212465133667 # # for c[5] = .576 a[5,1] = 2.272114264290177409193144938921415409241 a[5,2] = 0. a[5,3] = -8.526886447976398578316416192982602292786 a[5,4] = 6.830772183686221169123271254061186883545 # # for c[6] = .2272326564618766017153738192188229509142 a[6,1] = .5094385535389374394512668566783434123978e-1 a[6,2] = 0. a[6,3] = 0. a[6,4] = .1755865049809071110203693328749561646990 a[6,5] = .70229612707574674987780067603244497535e-3 # # for c[7] = .5407673435381233982846261807811770490858 a[7,1] = .1424783668683284782770955365543878809824 a[7,2] = 0. a[7,3] = 0. a[7,4] = -.3541799434668684104094753917518523845155 a[7,5] = .7595315450295100889001534202778550159932e-1 a[7,6] = .6765157656337123215269906939508560510196 # # for c[8] = .64 a[8,1] = .7111111111111111111111111111111111111111e-1 a[8,2] = 0. a[8,3] = 0. a[8,4] = 0. a[8,5] = 0. a[8,6] = .3279909287605898328568406057725491803016 a[8,7] = .2408979601282990560320482831163397085872 # # for c[9] = .48 a[9,1] = .7125e-1 a[9,2] = 0. a[9,3] = 0. a[9,4] = 0. a[9,5] = 0. a[9,6] = .3268842451575245554847578757216915662785 a[9,7] = .1156157548424754445152421242783084337215 a[9,8] = -.3375e-1 # # for c[10] = .6754e-1 a[10,1] = .4822677322465810178387112087673611111111e-1 a[10,2] = 0. a[10,3] = 0. a[10,4] = 0. a[10,5] = 0. a[10,6] = .3948559980495400110769549704186108167677e-1 a[10,7] = .1058851161934658144373823566907778072121 a[10,8] = -.2152006320474309346664428710937500000000e-1 a[10,9] = -.1045374260183348238623046875000000000000 # # for c[11] = .25 a[11,1] = -.2609113435754923412210928689962011065179e-1 a[11,2] = 0. a[11,3] = 0. a[11,4] = 0. a[11,5] = 0. a[11,6] = .3333333333333333333333333333333333333333e-1 a[11,7] = -.1652504006638105086724681598195267241410 a[11,8] = .3434664118368616658319419895678838776647e-1 a[11,9] = .1595758283215209043195814910843067811951 a[11,10] = .2140857321828193385584684233447183324979 # # for c[12] = .6770920153543242682384311058159603931192 a[12,1] = -.362842339625565859076509979091267105528e-1 a[12,2] = 0. a[12,3] = 0. a[12,4] = 0. a[12,5] = 0. a[12,6] = -1.096167597427208807028761474420297770752 a[12,7] = .1826035504321331052308236240517254331348 a[12,8] = .708225444417068325613028685455625123741e-1 a[12,9] = -.231364701848243126999929738482630407146e-1 a[12,10] = .2711204726320932916455631550463654973432 a[12,11] = 1.308133749422980744437146904349994472286 # # for c[13] = .8115 a[13,1] = -.5074635056416974879347823927726392374259 a[13,2] = 0. a[13,3] = 0. a[13,4] = 0. a[13,5] = 0. a[13,6] = -6.631342198657237090355284142048733580937 a[13,7] = -.252748010090880105270020973014860316405 a[13,8] = -.4952612380036095562991116175550167835424 a[13,9] = .293252554525388690285739720360003594753 a[13,10] = 1.440108693768280908474851998204423941413 a[13,11] = 6.237934498647055877243623886838802127716 a[13,12] = .7270192054526987638549835199880202544289 # # for c[14] = .906 a[14,1] = .6130118256955931701496387847232542148725 a[14,2] = 0. a[14,3] = 0. a[14,4] = 0. a[14,5] = 0. a[14,6] = 9.088803891640463313341034206647776279557 a[14,7] = -.407378815629344868103315381138325162923 a[14,8] = 1.790733389490374687043894756399015035977 a[14,9] = .714927166761755073724875250629602731782 a[14,10] = -1.438580857841722850237810322456327208949 a[14,11] = -8.263329312064740580595954649844133476994 a[14,12] = -1.537570570808865115231450725068826856201 a[14,13] = .3453832827564871699090880801079644428793 # # for c[15] = 1. a[15,1] = -1.211697910343873872490625222495537087293 a[15,2] = 0. a[15,3] = 0. a[15,4] = 0. a[15,5] = 0. a[15,6] = -19.05581871559595277753334676575234493500 a[15,7] = 1.26306067538987510135943101851905310045 a[15,8] = -6.913916969178458046793476128409110926069 a[15,9] = -.676462266509498065300115641383621209887 a[15,10] = 3.367860445026607887090352785684064242560 a[15,11] = 18.00675164312590810020103216906571965203 a[15,12] = 6.838828926794279896350389904990814350968 a[15,13] = -1.031516451921950498420447675652291096155 a[15,14] = .4129106232130622755368055554332539084021 # # for c[16] = 1. a[16,1] = 2.157389007494053627033175177985666660692 a[16,2] = 0. a[16,3] = 0. a[16,4] = 0. a[16,5] = 0. a[16,6] = 23.80712219809580523172312179815279712750 a[16,7] = .88627792492165554903036801415266308369 a[16,8] = 13.13913039759876381480201677314222971522 a[16,9] = -2.604415709287714883747369630937415176632 a[16,10] = -5.193859949783872300189266203049579105962 a[16,11] = -20.41234071154150778768154893536134356354 a[16,12] = -12.30085625250572261314889445241581039623 a[16,13] = 1.521553095008539362178397458330791655267 a[16,14] = 0. a[16,15] = 0. # # ******************************************************** # High order weights c[ 17] = 1 # ----------------------------------------------------------- # b[1] = .1458885278405539719101539582255752917034e-1 b[2] = 0. b[3] = 0. b[4] = 0. b[5] = 0. b[6] = 0. b[7] = 0. b[8] = .2024197887889332650566666683195656097825e-2 b[9] = .2178047084569716646796256135839225745895 b[10] = .1274895340854389692868677968654808668201 b[11] = .2244617745463131861258531547137348031621 b[12] = .1787254491259903095100090833796054447157 b[13] = .7594344758096557172908303416513173076283e-1 b[14] = .1294845879197561516869001434704642286297 b[15] = .2947744761261941714007911131590716605202e-1 b[16] = 0. # # ******************************************************** # Low order weights C[extra]:= 1 # -------------------------------------------------- # bh[1] = .2034666655224434599707885098832906986649e-1 bh[2] = 0. bh[3] = 0. bh[4] = 0. bh[5] = 0. bh[6] = 0. bh[7] = 0. bh[8] = 1.069617650982700109541321983413338230042 bh[9] = .7680834711303187278673130261850350530338e-1 bh[10] = .1130778186885240437498706751119241126785 bh[11] = .2552587357981962194892445789565762186511 bh[12] = -.9825898086919164036191607912120918904022 bh[13] = .3981545824421514217762002137442675068982 bh[14] = 0. bh[15] = 0. bh[16] = .4932600711506839027871318637915324696208e-1 # # ******************************************************* # # Largest coefficient in b or A has magnitude 23.80712 # # ******************************************************* # SUMMARY OF NORMS OF ERRORS: A101, A102, A10inf # ---------------------------------------------------- # A_[10, 1] = .6267198352e-5 # A_[10, 2] = .3511817004e-6 # A_[10,oo] = .6136631298e-7 #**************************************************** # # END OF GENERATION OF A PAIR OF RK METHODS # ############################################################# # # START OF GENERATION OF STABILITY INTERVALS # ############################################################# # # Stability Boundaries of High Order Method # ----------------------------------------- # Real Stability Interval is nearly [ -4.521447751, 0] # # Stability Boundaries of Low Order Method # ---------------------------------------- # Real Stability Interval is nearly [ -3.909402959, 0] # ############################################################## # # START OF GENERATION OF INTERPOLANT # #******************************************************* # # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 8 # # Coupling coefficients for c[17] = 1.0 a[17,1] = .1458885278405539719101539582255752917034e-1 a[17,2] = 0. a[17,3] = 0. a[17,4] = 0. a[17,5] = 0. a[17,6] = 0. a[17,7] = 0. a[17,8] = .2024197887889332650566666683195656097825e-2 a[17,9] = .2178047084569716646796256135839225745895 a[17,10] = .1274895340854389692868677968654808668201 a[17,11] = .2244617745463131861258531547137348031621 a[17,12] = .1787254491259903095100090833796054447157 a[17,13] = .7594344758096557172908303416513173076283e-1 a[17,14] = .1294845879197561516869001434704642286297 a[17,15] = .2947744761261941714007911131590716605202e-1 a[17,16] = 0. # #******************************************************** # # Coupling coefficients for c[18]:= .7421010083583088006243877166286162723673 # ---------------------------------------------------- a[18,1] = .1560140526108861651166696161636643678715e-1 a[18,2] = 0. a[18,3] = 0. a[18,4] = 0. a[18,5] = 0. a[18,6] = 0. a[18,7] = 0 a[18,8] = .2681164393327584462067257298507705692190 a[18,9] = .1883053124587791093781990103116496723062 a[18,10] = .1249199137461030776325034278436425745187 a[18,11] = .2302302127814521984877267202569592992854 a[18,12] = -.1360312216132798635363504089171114829643 a[18,13] = .7488659971306952790649243500419796404442e-1 a[18,14] = -.2812840029795629049644800354887547182869e-1 a[18,15] = -.2314455726481949553795911074427483913356e-1 a[18,16] = 0. a[18,17] = .2734530424111347407183095495529155013292e-1 # #******************************************************** # # Coupling coefficients for c[19]:= .888 # ---------------------------------------------------- a[19,1] = .1311195721844068401556584238625026007821e-1 a[19,2] = 0. a[19,3] = 0. a[19,4] = 0. a[19,5] = 0. a[19,6] = 0. a[19,7] = 0. a[19,8] = -.1464024265969826989710171144006401375029 a[19,9] = .2471264389666795959943268183777606168285 a[19,10] = .1311375203080032288323212687159488912255 a[19,11] = .2170560346982582529677346605154232633905 a[19,12] = .2867536713760320279685175119456430108611 a[19,13] = .2323311339149421811667180525022488323943e-1 a[19,14] = .5250677264199395668210993035986718117205e-1 a[19,15] = .2833951586009950740445688183974089075836e-2 a[19,16] = 0. a[19,17] = -.8502403851995712467765683685024083445736e-2 a[19,18] = .6914537026206649612108927235057202507752e-1 # #******************************************************** # # Coupling coefficients for c[20]:= .696 # ---------------------------------------------------- a[20,1] = .1398921213361768395172663025684236914687e-1 a[20,2] = 0. a[20,3] = 0. a[20,4] = 0. a[20,5] = 0. a[20,6] = 0. a[20,7] = 0. a[20,8] = -.3157406517950500155656872013463001170279e-1 a[20,9] = .2271812513272158193884043729886141068401 a[20,10] = .1289486410996786560165007139967355200862 a[20,11] = .2216682589135277018738330104776507206003 a[20,12] = .1948368236542480784645408517950426740505 a[20,13] = .5740088404417652948912844658374513373184e-1 a[20,14] = .9008366542675954700472151691971957675586e-1 a[20,15] = .1579153208844212165580559397387558558087e-1 a[20,16] = 0. a[20,17] = -.1899131505909185814243914464042645862057e-1 a[20,18] = -.8830926811918835070775190595441414629725e-1 a[20,19] = -.1150256203298809274379013662627550701719 # #******************************************************** # # Coupling coefficients for c[21]:= .487 # ---------------------------------------------------- a[21,1] = .1615147291900762304051270768727488699116e-1 a[21,2] = 0. a[21,3] = 0. a[21,4] = 0. a[21,5] = 0. a[21,6] = 0. a[21,7] = 0. a[21,8] = .8098685003242905691737114344809608208533e-1 a[21,9] = .1276916294306930449548063682447180310200 a[21,10] = .1234814359383480575498127887662911829596 a[21,11] = .2339851259140109824702007335541675692697 a[21,12] = -.6595995683357367659329999201079842018819e-1 a[21,13] = -.2565276859406432791053055820612070574951e-1 a[21,14] = -.1258973463819247076247947215937788425689 a[21,15] = -.4307672490364843615025132534342781501874e-1 a[21,16] = 0. a[21,17] = .4973042479196705159702504356466546825472e-1 a[21,18] = .1000473540179392626782905455570668634250 a[21,19] = .1378658806763623213069940499298119480365 a[21,20] = -.1223533770075462522361367835979662485167 # -------------------------------------------------------- # COEFFICIENTS FOR INTERPOLANT bi8 WITH 21 STAGES # -------------------------------------------------------- # # COEFFICIENTS OF bi8[1] bi8[1,1] = 1. u bi8[1,2] = -12.75304069282388950483064356409920964903 u^2 bi8[1,3] = 68.54470113831162103032818060021729044674 u^3 bi8[1,4] = -194.8086610529652454702496599846926584629 u^4 bi8[1,5] = 317.7392440058917273091720330437842255568 u^5 bi8[1,6] = -299.5110317016553611442365899609354277447 u^6 bi8[1,7] = 151.9504248851541972968268022793780785647 u^7 bi8[1,8] = -32.14704772912899411981910701782974118232 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[2] bi8[2,1] = 0. u bi8[2,2] = 0. u^2 bi8[2,3] = 0. u^3 bi8[2,4] = 0. u^4 bi8[2,5] = 0. u^5 bi8[2,6] = 0. u^6 bi8[2,7] = 0. u^7 bi8[2,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[3] bi8[3,1] = 0. u bi8[3,2] = 0. u^2 bi8[3,3] = 0. u^3 bi8[3,4] = 0. u^4 bi8[3,5] = 0. u^5 bi8[3,6] = 0. u^6 bi8[3,7] = 0. u^7 bi8[3,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[4] bi8[4,1] = 0. u bi8[4,2] = 0. u^2 bi8[4,3] = 0. u^3 bi8[4,4] = 0. u^4 bi8[4,5] = 0. u^5 bi8[4,6] = 0. u^6 bi8[4,7] = 0. u^7 bi8[4,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[5] bi8[5,1] = 0. u bi8[5,2] = 0. u^2 bi8[5,3] = 0. u^3 bi8[5,4] = 0. u^4 bi8[5,5] = 0. u^5 bi8[5,6] = 0. u^6 bi8[5,7] = 0. u^7 bi8[5,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[6] bi8[6,1] = 0. u bi8[6,2] = 0. u^2 bi8[6,3] = 0. u^3 bi8[6,4] = 0. u^4 bi8[6,5] = 0. u^5 bi8[6,6] = 0. u^6 bi8[6,7] = 0. u^7 bi8[6,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[7] bi8[7,1] = 0. u bi8[7,2] = 0. u^2 bi8[7,3] = 0. u^3 bi8[7,4] = 0. u^4 bi8[7,5] = 0. u^5 bi8[7,6] = 0. u^6 bi8[7,7] = 0. u^7 bi8[7,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[8] bi8[8,1] = 0. u bi8[8,2] = -.7205785602508598770412906345635211707530 u^2 bi8[8,3] = 6.559119452090996226782640921071801708575 u^3 bi8[8,4] = -23.65417183348355244612060745867113623926 u^4 bi8[8,5] = 44.16895609281556502164197054695369477469 u^5 bi8[8,6] = -45.39036357573745767095716350329312304563 u^6 bi8[8,7] = 24.43461389111572285100991773589739045465 u^7 bi8[8,8] = -5.395551268662524772664900940711910826177 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[9] bi8[9,1] = 0. u bi8[9,2] = -48.06969107148755163304089843112677204750 u^2 bi8[9,3] = 451.8280048138745279924509263176669733181 u^3 bi8[9,4] = -1652.497181212881040972312045847339995538 u^4 bi8[9,5] = 3109.740640759030910750811309301753788556 u^5 bi8[9,6] = -3211.322751886536222454319056864879758831 u^6 bi8[9,7] = 1734.432866374712319698880133120955280438 u^7 bi8[9,8] = -383.8940830682559717177907419834455933213 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[10] bi8[10,1] = 0. u bi8[10,2] = 16.32345788425353372538518290168630386345 u^2 bi8[10,3] = -118.7000544943430560099961188668917723161 u^3 bi8[10,4] = 379.7566858308294928207030358265089540700 u^4 bi8[10,5] = -658.7110535057816543655898314260197627370 u^5 bi8[10,6] = 644.2805206048469902599556429935393520064 u^6 bi8[10,7] = -334.8751825767893992539894957157903467478 u^7 bi8[10,8] = 72.05311579106953179281845208383275272780 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[11] bi8[11,1] = 0. u bi8[11,2] = -5.888504109270884968456670963647316074790 u^2 bi8[11,3] = 89.44704113715942232261735606938508401319 u^3 bi8[11,4] = -380.5212519133325379643523316755978956588 u^4 bi8[11,5] = 770.9937272473377188110779497353201847420 u^5 bi8[11,6] = -831.4716893548379599332950159082545018560 u^6 bi8[11,7] = 461.9387177871916189774255799856083869291 u^7 bi8[11,8] = -104.2735790197010640588910140881002072916 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[12] bi8[12,1] = 0. u bi8[12,2] = -69.22821100686856642029708151339949374410 u^2 bi8[12,3] = 627.4402883568152894700875088172124339413 u^3 bi8[12,4] = -2258.351433966898561277167615407280413114 u^4 bi8[12,5] = 4212.395800215491820633428188331388768232 u^5 bi8[12,6] = -4325.916149192490627782429268979382924699 u^6 bi8[12,7] = 2327.648261456242912420669452255092833474 u^7 bi8[12,8] = -513.8098304131662767347811744202515986459 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[13] bi8[13,1] = 0. u bi8[13,2] = -38.04668072585188932845088326881300565231 u^2 bi8[13,3] = 340.9894379782233715580222226199659613703 u^3 bi8[13,4] = -1221.089637320158271327850635113537223709 u^4 bi8[13,5] = 2271.121533555259071203608357605468537656 u^5 bi8[13,6] = -2328.099120585713191256845645730711618239 u^6 bi8[13,7] = 1251.132631830924456968695609885535799254 u^7 bi8[13,8] = -275.9322212851025822454499429637433189491 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[14] bi8[14,1] = 0. u bi8[14,2] = -75.21598899610186748511604166683735788867 u^2 bi8[14,3] = 670.5551756563966247587443735545005782764 u^3 bi8[14,4] = -2395.425253052829223230171636642290078449 u^4 bi8[14,5] = 4449.143231627101738352915330060972953361 u^5 bi8[14,6] = -4556.769050179329341174034103718438911683 u^6 bi8[14,7] = 2447.365350086656490540478347199404246857 u^7 bi8[14,8] = -539.5239805539746656111293686438409662456 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[15] bi8[15,1] = 0. u bi8[15,2] = -19.46588639117053206710108537195779499764 u^2 bi8[15,3] = 172.8442419404515527792492527636420780662 u^3 bi8[15,4] = -616.3040486605512589130986770456245791880 u^4 bi8[15,5] = 1143.483637444009748019174885933341490497 u^5 bi8[15,6] = -1170.357669638643781845251579162353094100 u^6 bi8[15,7] = 628.2905498131297391288540900112436704439 u^7 bi8[15,8] = -138.4613470596128476846868080169758635556 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[16] bi8[16,1] = 0. u bi8[16,2] = 0. u^2 bi8[16,3] = 0. u^3 bi8[16,4] = 0. u^4 bi8[16,5] = 0. u^5 bi8[16,6] = 0. u^6 bi8[16,7] = 0. u^7 bi8[16,8] = 0. u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[17] bi8[17,1] = 0. u bi8[17,2] = 22.25276964616901764060657108171977843291 u^2 bi8[17,3] = -202.2239493340537483960420170974810960961 u^3 bi8[17,4] = 741.1380586926791133828821084525361362850 u^4 bi8[17,5] = -1419.345991543901288934527221623894382397 u^5 bi8[17,6] = 1505.723453115174938364140876028053730124 u^6 bi8[17,7] = -841.3580375761078273196578619974820483141 u^7 bi8[17,8] = 193.8136970000397952625975451565478819654 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[18] bi8[18,1] = 0. u bi8[18,2] = 14.38227638804283974976194859491865842966 u^2 bi8[18,3] = -301.8862921284913174289877784920239768093 u^3 bi8[18,4] = 1781.158815560130838385479471257488378388 u^4 bi8[18,5] = -4706.785555404445608825447884178551282728 u^5 bi8[18,6] = 6291.645831877559252216657958850293660213 u^6 bi8[18,7] = -4164.432457468105482852522949304279052327 u^7 bi8[18,8] = 1085.917381175309478755059233272153614833 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[19] bi8[19,1] = 0. u bi8[19,2] = 94.92756297288050252130347529152607755873 u^2 bi8[19,3] = -819.3810521264963242304829331408227079441 u^3 bi8[19,4] = 2811.287710727701073955763185548552769132 u^4 bi8[19,5] = -4973.994583541372152306531194715881127387 u^5 bi8[19,6] = 4810.867980444981597632278117658725359609 u^6 bi8[19,7] = -2417.563170381452428143421579409061339218 u^7 bi8[19,8] = 493.8555519037577305710909287669609682492 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[20] bi8[20,1] = 0. u bi8[20,2] = 63.97757128518312942674385099931772857860 u^2 bi8[20,3] = -398.4710369466142415586467341825347335632 u^3 bi8[20,4] = 716.5966869905804904541294272473572154569 u^4 bi8[20,5] = 52.89052166461839778508215175982407959882 u^5 bi8[20,6] = -1470.500844962700814722191656818947551329 u^6 bi8[20,7] = 1524.433133991196905505389714285761298379 u^7 bi8[20,8] = -488.9260320222638668905067532907780371207 u^8 # -------------------------------------------------------- # # COEFFICIENTS OF bi8[21] bi8[21,1] = 0. u bi8[21,2] = 57.52494337729701822053356654527592436144 u^2 bi8[21,3] = -587.5456254433247185141268798839079144120 u^3 bi8[21,4] = 2312.713681211178682602365980842590527027 u^4 bi8[21,5] = -4612.840108616055993454816044374461167725 u^5 bi8[21,6] = 4986.820885035081979510527485116584809575 u^6 bi8[21,7] = -2793.397702113869225818637760332264198189 u^7 bi8[21,8] = 636.7239265496922574541536520861820193631 u^8 # #******************************************************** # # FIVE ADDITIONAL STAGES FOR INTERPOLANT OF ORDER 9 # # Coupling coefficients for c[22]:= .025 # ---------------------------------------------------- a[22,1] = .1802729411106818689763249275362776542125e-1 a[22,2] = 0. a[22,3] = 0. a[22,4] = 0. a[22,5] = 0. a[22,6] = 0. a[22,7] = 0. a[22,8] = -.3566948654464566871345751863957855326182e-3 a[22,9] = -.2359965598171250974225291789331305531887e-1 a[22,10] = .8489537818582623161952771938798430467577e-2 a[22,11] = -.2424017121415795431658865084807451176669e-2 a[22,12] = -.3430595122831044180368089698215097859892e-1 a[22,13] = -.1890658549297046191788725638037661418072e-1 a[22,14] = -.3742593046527093615091178254251506793186e-1 a[22,15] = -.9695346568972416886241067894611986071147e-2 a[22,16] = 0. a[22,17] = .1102424057658581840569553621781637903330e-1 a[22,18] = .4923260682022719983443039400621144750980e-2 a[22,19] = .4757764286275925144559532694675125937637e-1 a[22,20] = .3403995941160684337366745033612222756612e-1 a[22,21] = .2763224626147357535178074437043373219519e-1 # #******************************************************** # # Coupling coefficients for c[23]:= .15 # ---------------------------------------------------- a[23,1] = .1674115470096526424930400903558890871308e-1 a[23,2] = 0. a[23,3] = 0. a[23,4] = 0. a[23,5] = 0. a[23,6] = 0. a[23,7] = 0. a[23,8] = -.3173492444543278603351394583591742321103e-2 a[23,9] = -.1907932208630995154539013764218262860213 a[23,10] = .1156811286400889022914973296917837873123 a[23,11] = .2659243297776452866445546052304774936345e-1 a[23,12] = -.3088649490220827144035155968652816431108 a[23,13] = -.1753758456547022422433014122559418385679 a[23,14] = -.3519244231945119122948228740531438774071 a[23,15] = -.9209686132127586046007074704921651582851e-1 a[23,16] = 0. a[23,17] = .1013643084710043289094345867037510169960 a[23,18] = -.8614613115672610072132806092797279629388e-1 a[23,19] = .4667555353741319512606533809977766283817 a[23,20] = .4471784578431838563500095104120691993359 a[23,21] = .1840619056498027924549371847929574094481 a[23,22] = 0. # #******************************************************** # # Coupling coefficients for c[24]:= .32 # ---------------------------------------------------- a[24,1] = .1067816157945957352545935273312729770712e-1 a[24,2] = 0. a[24,3] = 0. a[24,4] = 0. a[24,5] = 0. a[24,6] = 0. a[24,7] = 0. a[24,8] = .3813266550650219306405894185406227733203e-3 a[24,9] = .9563838511927889653937246525395111512962e-1 a[24,10] = .1383796710757440233248935289235401276023 a[24,11] = .1794589653248393403412396094337145578219 a[24,12] = .2328104103984205159658342243398415303992e-1 a[24,13] = -.6102337776291304739559151883232786325123e-2 a[24,14] = -.2957864564982467043648509518504953052119e-1 a[24,15] = -.1107556819372404441098997386306135386770e-1 a[24,16] = 0. a[24,17] = .1005006241909649985189552106106942758409e-1 a[24,18] = -.9189958889836397344227776088639708677529e-1 a[24,19] = .4889782809929091409586999965373170403839e-1 a[24,20] = .7683137001604329651351035116374049373690e-1 a[24,21] = -.1249406708104556246901528582576587419443 a[24,22] = 0. a[24,23] = 0. # #******************************************************** # # Coupling coefficients for c[25]:= .78 # ---------------------------------------------------- a[25,1] = .1407873162514538134880663877417425640142e-1 a[25,2] = 0. a[25,3] = 0. a[25,4] = 0. a[25,5] = 0. a[25,6] = 0. a[25,7] = 0. a[25,8] = .1921038236500748458986816137745896655262e-2 a[25,9] = .2103911064595803591331678030844204745297 a[25,10] = .1287126282116406147526805293017325463897 a[25,11] = .2222827890207636907592258288998389315181 a[25,12] = .1689157537655836922893273799046879855404 a[25,13] = .7069536651338852930255328632439555742574e-1 a[25,14] = .1192421401475245249188274865443088811860 a[25,15] = .2685261833359796204499227534872501897484e-1 a[25,16] = 0. a[25,17] = -.3077554523024171431258004671769555940844e-1 a[25,18] = .8284466445798771733365157887905394914006e-2 a[25,19] = -.1535503041842782550897093173814614623206 a[25,20] = -.2150191510960740019354801525582536987010e-1 a[25,21] = .1445112576460309485390417714704744806405e-1 a[25,22] = 0. a[25,23] = 0. a[25,24] = 0. # #******************************************************** # # Coupling coefficients for c[26]:= .96 # ---------------------------------------------------- a[26,1] = .1422598489194661552790199000685205084824e-1 a[26,2] = 0. a[26,3] = 0. a[26,4] = 0. a[26,5] = 0. a[26,6] = 0. a[26,7] = 0. a[26,8] = .1949172492119241778367670693682637328188e-2 a[26,9] = .2124063537210806078797518674148478107397 a[26,10] = .1283651739828476111356431808186160040103 a[26,11] = .2228603986302258483512559751598074395656 a[26,12] = .1715923679711209630782228726709623464662 a[26,13] = .7212912939761323676316514664066037355886e-1 a[26,14] = .1220420686370054673857430981768668520159 a[26,15] = .2757049488622773377977068820958406578502e-1 a[26,16] = 0. a[26,17] = -.2399703787121476720950542355073551377435e-1 a[26,18] = .5371225309992069259478306291407462056681e-1 a[26,19] = -.1761964270699028520222472394692440648034e-1 a[26,20] = -.3622477925515253053764132865960991436725e-1 a[26,21] = .1098806212324956467476592345131563373716e-1 a[26,22] = 0. a[26,23] = 0. a[26,24] = 0. a[26,25] = 0. # # -------------------------------------------------------- # COEFFICIENTS FOR INTERPOLANT bi59, WITH, 26, STAGES # -------------------------------------------------------- # # COEFFICIENTS OF bi9[1] bi9[1,1] = 1. u bi9[1,2] = -28.32690107549798096690906467156557638494 u^2 bi9[1,3] = 257.5220844783513822655991530565675221343 u^3 bi9[1,4] = -1150.934922587486676595644173070427734578 u^4 bi9[1,5] = 2904.420880778592699327677577124946402676 u^5 bi9[1,6] = -4344.528637462060406744624584680230498732 u^6 bi9[1,7] = 3822.157475253294982131000232331976202139 u^7 bi9[1,8] = -1828.450847963912086611128480846950926244 u^8 bi9[1,9] = 367.1554574315021425912203561515071665187 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[2] bi9[2,1] = 0. u bi9[2,2] = 0. u^2 bi9[2,3] = 0. u^3 bi9[2,4] = 0. u^4 bi9[2,5] = 0. u^5 bi9[2,6] = 0. u^6 bi9[2,7] = 0. u^7 bi9[2,8] = 0. u^8 bi9[2,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[3] bi9[3,1] = 0. u bi9[3,2] = 0. u^2 bi9[3,3] = 0. u^3 bi9[3,4] = 0. u^4 bi9[3,5] = 0. u^5 bi9[3,6] = 0. u^6 bi9[3,7] = 0. u^7 bi9[3,8] = 0. u^8 bi9[3,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[4] bi9[4,1] = 0. u bi9[4,2] = 0. u^2 bi9[4,3] = 0. u^3 bi9[4,4] = 0. u^4 bi9[4,5] = 0. u^5 bi9[4,6] = 0. u^6 bi9[4,7] = 0. u^7 bi9[4,8] = 0. u^8 bi9[4,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[5] bi9[5,1] = 0. u bi9[5,2] = 0. u^2 bi9[5,3] = 0. u^3 bi9[5,4] = 0. u^4 bi9[5,5] = 0. u^5 bi9[5,6] = 0. u^6 bi9[5,7] = 0. u^7 bi9[5,8] = 0. u^8 bi9[5,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[6] bi9[6,1] = 0. u bi9[6,2] = 0. u^2 bi9[6,3] = 0. u^3 bi9[6,4] = 0. u^4 bi9[6,5] = 0. u^5 bi9[6,6] = 0. u^6 bi9[6,7] = 0. u^7 bi9[6,8] = 0. u^8 bi9[6,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[7] bi9[7,1] = 0. u bi9[7,2] = 0. u^2 bi9[7,3] = 0. u^3 bi9[7,4] = 0. u^4 bi9[7,5] = 0. u^5 bi9[7,6] = 0. u^6 bi9[7,7] = 0. u^7 bi9[7,8] = 0. u^8 bi9[7,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[8] bi9[8,1] = 0. u bi9[8,2] = -.1352877251970476367599723128957774732408e-1 u^2 bi9[8,3] = .4916573392696415374272244679017622556033 u^3 bi9[8,4] = -4.436464950699828531781508575523369430923 u^4 bi9[8,5] = 17.31944616187202911483010888269388372950 u^5 bi9[8,6] = -34.64102686818872098410895454499691544074 u^6 bi9[8,7] = 37.38281301815147188288272397739134884003 u^7 bi9[8,8] = -20.77503017271466649882774316118540751870 u^8 bi9[8,9] = 4.674158442717667575904712851691470968655 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[9] bi9[9,1] = 0. u bi9[9,2] = -1.455702711708433893360889952963683899055 u^2 bi9[9,3] = 52.90257641362051900920717423116250315520 u^3 bi9[9,4] = -477.3658548642740885503090276141543695104 u^4 bi9[9,5] = 1863.581097723678565157175620323663884432 u^5 bi9[9,6] = -3727.391873500693602119215981342643938177 u^6 bi9[9,7] = 4022.409439034606738749309726708688089035 u^7 bi9[9,8] = -2235.403671264127820837729037807301982183 u^8 bi9[9,9] = 502.9417938773550941496020410671334197216 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[10] bi9[10,1] = 0. u bi9[10,2] = -.8520791942350588325316811661249358984267 u^2 bi9[10,3] = 30.96592753514428792162712738493044327388 u^3 bi9[10,4] = -279.4207290379426863235594737603660800207 u^4 bi9[10,5] = 1090.826215660802050077745313656212911679 u^5 bi9[10,6] = -2181.786870784446576299842227492445932780 u^6 bi9[10,7] = 2354.472081510133899345761960831178682917 u^7 bi9[10,8] = -1308.468373164874203463640310982959594658 u^8 bi9[10,9] = 294.3913170095037265437261593264399863548 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[11] bi9[11,1] = 0. u bi9[11,2] = -1.500195363988222220268242336906771952014 u^2 bi9[11,3] = 54.51951091415031705577508793820940519869 u^3 bi9[11,4] = -491.9562467209968998612925445316083084741 u^4 bi9[11,5] = 1920.540300388688941881662910323125894192 u^5 bi9[11,6] = -3841.317298798240146027659208409462769610 u^6 bi9[11,7] = 4145.351893602041132240186825905054310664 u^7 bi9[11,8] = -2303.727400725200622735225098094667761194 u^8 bi9[11,9] = 518.3138984780918128529461223609697359788 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[12] bi9[12,1] = 0. u bi9[12,2] = -1.194515595127319561381305768593050066673 u^2 bi9[12,3] = 43.41061676962890600957969169570693466384 u^3 bi9[12,4] = -391.7152545161095434284638812068808832220 u^4 bi9[12,5] = 1529.211058075771098268564306266892199838 u^5 bi9[12,6] = -3058.610584589748864431933436681187353637 u^6 bi9[12,7] = 3300.695098159947454006902079837506257710 u^7 bi9[12,8] = -1834.319964682933276992160596708288646267 u^8 bi9[12,9] = 412.7022718276975364384031516482241464250 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[13] bi9[13,1] = 0. u bi9[13,2] = -.5075697553248201181074098453886297230598 u^2 bi9[13,3] = 18.44590076692263941141687424224337726427 u^3 bi9[13,4] = -166.4463960979508832639844199618200121315 u^4 bi9[13,5] = 649.7874835236435459733721670731119363679 u^5 bi9[13,6] = -1299.655050454701135142040066484507391334 u^6 bi9[13,7] = 1402.520829538696240143275819971522246250 u^7 bi9[13,8] = -779.4333866041422479301856382011236732598 u^8 bi9[13,9] = 175.3641325304376264979817562401272782969 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[14] bi9[14,1] = 0. u bi9[14,2] = -.8654131818113355423508731936492899184395 u^2 bi9[14,3] = 31.45050607647596882232093808213268629209 u^3 bi9[14,4] = -283.7933185281612362330622863936794365142 u^4 bi9[14,5] = 1107.896299411122562578451965902519939840 u^5 bi9[14,6] = -2215.929142096727917414601771920960325991 u^6 bi9[14,7] = 2391.316663206240712062204317538883819427 u^7 bi9[14,8] = -1328.944288020880399801387165802586147935 u^8 bi9[14,9] = 298.9981777216614016801117759308092190290 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[15] bi9[15,1] = 0. u bi9[15,2] = -.1970131900633844007334057633668821082292 u^2 bi9[15,3] = 7.159776002331775566615895079547238582865 u^3 bi9[15,4] = -64.60616521334211261463809724329663463146 u^4 bi9[15,5] = 252.2149983312684580977777634191997994167 u^5 bi9[15,6] = -504.4610810354733798936380034445989591939 u^6 bi9[15,7] = 544.3884310658628635840232552836991532528 u^7 bi9[15,8] = -302.5370529387022446453538858257895456787 u^8 bi9[15,9] = 68.06758442573064372308655760592173752592 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[16] bi9[16,1] = 0. u bi9[16,2] = 0. u^2 bi9[16,3] = 0. u^3 bi9[16,4] = 0. u^4 bi9[16,5] = 0. u^5 bi9[16,6] = 0. u^6 bi9[16,7] = 0. u^7 bi9[16,8] = 0. u^8 bi9[16,9] = 0. u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[17] bi9[17,1] = 0. u bi9[17,2] = -.4541849829711136730965001627668694658569 u^2 bi9[17,3] = 16.70127113669635686632210799083284772387 u^3 bi9[17,4] = -156.7717275533304690372380410971653223970 u^4 bi9[17,5] = 651.5466733893466243333417542222872994634 u^5 bi9[17,6] = -1412.320009571548049765391447883772301354 u^6 bi9[17,7] = 1667.138515616290965031624809891756516568 u^7 bi9[17,8] = -1017.673390248052278400509234341147715025 u^8 bi9[17,9] = 251.8328522135679646449465513799755444867 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[18] bi9[18,1] = 0. u bi9[18,2] = -.1642163800536330788290065204813354321587 u^2 bi9[18,3] = 6.019579370077226689069574595580851814148 u^3 bi9[18,4] = -55.91040567458732377701366184031595554429 u^4 bi9[18,5] = 228.2688656052759709055637645192366232716 u^5 bi9[18,6] = -482.2012255868892821374987074119730578621 u^6 bi9[18,7] = 550.0371698613109364952968030491813233723 u^7 bi9[18,8] = -321.9620585702092198978986346679259513831 u^8 bi9[18,9] = 75.91229137507532480130986827669750176353 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[19] bi9[19,1] = 0. u bi9[19,2] = -.6748844193125564745929227754653454960000 u^2 bi9[19,3] = 24.73882523992791864853900738883002952509 u^3 bi9[19,4] = -229.7764793920052818752970771400892244362 u^4 bi9[19,5] = 938.1226206596337368237001113946238849141 u^5 bi9[19,6] = -1981.715185876861586680601839010172967024 u^6 bi9[19,7] = 2260.502368039869828842019362146467672844 u^7 bi9[19,8] = -1323.176024632043052129631852045188620769 u^8 bi9[19,9] = 311.9787603807909928458652100409945704424 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[20] bi9[20,1] = 0. u bi9[20,2] = 1.778873344420799933681245486496450242333 u^2 bi9[20,3] = -65.20707180707839471257988195976352818886 u^3 bi9[20,4] = 605.6492677392717373735460695165094586719 u^4 bi9[20,5] = -2472.721663050785177698018480246117915238 u^5 bi9[20,6] = 5223.443036336624954800506019083890195002 u^6 bi9[20,7] = -5958.275657929989312761065969519200553937 u^7 bi9[20,8] = 3487.652837788410553784668028541760907900 u^8 bi9[20,9] = -822.3196224208751607207370309035750144516 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[21] bi9[21,1] = 0. u bi9[21,2] = .4134694024574781779455481610866606179516e-1 u^2 bi9[21,3] = -1.515629491027822593270509776882854629852 u^3 bi9[21,4] = 14.07730581923479579079647554513401058020 u^4 bi9[21,5] = -57.47428571415020809167337188499668618053 u^5 bi9[21,6] = 121.4102104446333031674235730516273787671 u^6 bi9[21,7] = -138.4901675933193250049116011300805636609 u^7 bi9[21,8] = 81.06466597761229475532476786813214818827 u^8 bi9[21,9] = -19.11344638322878584148388848904209912604 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[22] bi9[22,1] = 0. u bi9[22,2] = 31.31247017428404500084714290987346868154 u^2 bi9[22,3] = -355.3157275297828193986043583116719602750 u^3 bi9[22,4] = 1749.514715230440391833447109626876044060 u^4 bi9[22,5] = -4695.147622413440114700018050785658067772 u^5 bi9[22,6] = 7343.556109316445935223022259185814180962 u^6 bi9[22,7] = -6685.313457191056010094751616991682515277 u^7 bi9[22,8] = 3285.682573893041315538969260935092019337 u^8 bi9[22,9] = -674.2890614799327434029117465686431697155 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[23] bi9[23,1] = 0. u bi9[23,2] = -2.730958729620607116715051590434636562839 u^2 bi9[23,3] = 87.05655731583556409257744115400887223561 u^3 bi9[23,4] = -458.0573888328072551306550581455931677106 u^4 bi9[23,5] = 1030.528220479689242604149818460447661881 u^5 bi9[23,6] = -1166.915434857878624822018690873819596210 u^6 bi9[23,7] = 648.4882950191960598212061502166901796605 u^7 bi9[23,8] = -131.2788560071460746781394967167571571369 u^8 bi9[23,9] = -7.090434387268304770405112504542156157026 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[24] bi9[24,1] = 0. u bi9[24,2] = 3.159813308843413258842148106168074297225 u^2 bi9[24,3] = -113.1719939045261456697649954642662011379 u^3 bi9[24,4] = 972.1689485848533047356437130956206690979 u^4 bi9[24,5] = -3550.940444875616705777455788680914067679 u^5 bi9[24,6] = 6713.264174671284729472235882859103511748 u^6 bi9[24,7] = -6928.875337321575454509723879737501297631 u^7 bi9[24,8] = 3717.788457472750001241039636185665671993 u^8 bi9[24,9] = -813.3936179360131427508167163638763606878 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[25] bi9[25,1] = 0. u bi9[25,2] = .9128020953320920409453895709005633217150 u^2 bi9[25,3] = -32.82005802633989134102763080315293143973 u^3 bi9[25,4] = 285.2155813990437864609136220241490714545 u^4 bi9[25,5] = -1042.591339563443951766186011126488373870 u^5 bi9[25,6] = 1892.181696336440909747003099385298260399 u^6 bi9[25,7] = -1796.360453156949035787162250294203369024 u^7 bi9[25,8] = 850.9940020538469208530391946403337404454 u^8 bi9[25,9] = -157.5322311379308302075254133968369612868 u^9 # -------------------------------------------------------- # # COEFFICIENTS OF bi9[26] bi9[26,1] = 0. u bi9[26,2] = 1.731857489108072590441870089449362050412 u^2 bi9[26,3] = -63.35430859967743018082992099191699844809 u^3 bi9[26,4] = 584.5655351968502690285922607726312447369 u^4 bi9[26,5] = -2365.388804571949367110661478844787210962 u^5 bi9[26,6] = 4957.618194378028460052984086615038480468 u^6 bi9[26,7] = -5639.545999732754146178078750017327503148 u^7 bi9[26,8] = 3312.967807809277108448776287030888641389 u^8 bi9[26,9] = -788.5942819688829666512243546539760160873 u^9 # #******************************************************** # Norms of low order INTERPOLANT coefficients on [0,2] # u Max norm 2-norm #------------------------------------------------- 0.1000000000 -.3369393702e-6 .7987461718e-6 0.2000000000 -.1864275619e-6 .7392738861e-6 0.3000000000 .2935083832e-6 .7071101564e-6 0.4000000000 .1211173854e-6 .3629492663e-6 0.5000000000 .1466029037e-6 .4423516451e-6 0.6000000000 .2107692480e-6 .3649580859e-6 0.7000000000 .3800489063e-6 .4979708722e-6 0.8000000000 .8403104476e-7 .3202136242e-6 0.9000000000 -.3861088313e-6, .6547298470e-6 1.000000000 -.1729750000e-56 .2912300470e-56 1.1000000000 -.4849412617e-5 .8567610375e-5 1.2000000000 -.4616961427e-4 .8864106428e-4 1.3000000000 -.2175564798e-3 .4576362120e-3 1.4000000000 -.7392784253e-3 .1706376682e-2 1.5000000000 -.2059810063e-2 .5207332843e-2 1.6000000000 -.5006074926e-2 .1381383757e-1 1.7000000000 -.1099531810e-1 .3298138883e-1 1.8000000000 -.2232294213e-1 .7247614310e-1 1.9000000000 .4520073653e-1 .1488735805 2.0000000000 .8875859851e-1 .2890920753 #******************************************************** # Norms of high order INTERPOLANT coefficients on [0,2] # u Max norm 2-norm #------------------------------------------------- 0.1000000000 -.1806941467e-7 .6135898130e-7 0.2000000000 -.3958613882e-7 .1184785790e-6 0.3000000000 -.4457664035e-7 .1597247470e-6 0.4000000000 -.4577917562e-7 .1685013416e-6 0.5000000000 -.4531503984e-7 .2534864991e-6 0.6000000000 -.5381004627e-7 .3197041267e-6 0.7000000000 -.5586493403e-7 .3200346836e-6 0.8000000000 .6691082789e-7 .3299034248e-6 0.9000000000 -.5978201841e-7 .3409933691e-6 1.0000000000 -.6136631298e-7 .3511817004e-6 1.1000000000 .2719278385e-6 .1347723555e-5 1.2000000000 .4925463773e-5 .2163656136e-4 1.3000000000 .3502851146e-4 .1522338904e-3 1.4000000000 .1650823884e-3 .7134653643e-3 1.5000000000 .6053665235e-3 .2606122498e-2 1.6000000000 .1866465335e-2 .8011731267e-2 1.7000000000 .5059572459e-2 .2166900316e-1 1.8000000000 .1240843091e-1 .5304762159e-1 1.9000000000 .2807634340e-1 .1198571186 2.0000000000 .5944516861e-1 .2534701080 #********************************************************#