%
%  w02char.m - characteristic solution (djm: 15 sept 10)
%

%  clear everything & set parameters
clear;  close all

%  coordinates
xL = 1;  xx = -xL:xL/100:xL;
yL = 2;  yy = -yL:yL/100:yL;

%  make matrices of coordinates (type "help meshgrid")
[xg, yg] = meshgrid(xx,yy);

%  PDE solution, matrix of values
ug = yg - asin(xg);

%  surface plot
figure(1);  clf
surf(xx,yy,ug);  shading flat

xlabel('\bf x-axis')
ylabel('\bf y-axis')
zlabel('\bf u-axis')
title('\bf surface plot of solution to s1.2, #6')
colorbar

%  optional characteristics
hold on
if(1==1)
    for kk = [-2*yL:0.5:2*yL]
       yc = kk + asin(xx);
       list = find(yc >= -yL);  yc = yc(list);
       list = find(yc <=  yL);  yc = yc(list);
       plot3(sin(yc-kk),yc,kk*ones(size(yc)),'k')     
    end
    axis([-xL xL -yL yL -2*yL 2*yL])
end
    
%  contour plot of characteristics
figure(2);  clf
contour(xx,yy,ug,[-2*yL:0.5:2*yL])

xlabel('\bf x-axis')
ylabel('\bf y-axis')
title('\bf contour plot of characteristics')
colorbar