%
%  w05diff.m - diffusion solutions (djm: 04 oct 2010)
%   

Lx = 5;  dx = Lx/200;
xp = dx:dx:Lx;
xx = [-Lx:dx:Lx];

figure(1);  clf
subplot(2,1,1)
for tt = [(1:6).^2]
    plot(xx,(1+erf(xx/sqrt(tt)))/2,'r');  hold on
end

plot( xp, ones(size(xp)),'k','linewidth',2)
plot(-xp,zeros(size(xp)),'k','linewidth',2)
plot([0 0],[0 1],'ko')
plot([0],[1/2],'k.')

axis([-Lx Lx -0.1 1.1])

title('\bf similarity-based diffusion solutions')
ylabel('\bf Q(x,t)')
xlabel('\bf x-axis')
text(-0.2,0.8 ,'t = 1')
text( 3.0,0.65,'t = 36')


subplot(2,1,2)
for tt = [(1:6).^(-2)]
    plot(xx,exp(-(xx/(4*tt)).^2)/sqrt(4*tt)/sqrt(pi),'r');  hold on
end

axis([-Lx Lx -0.1 2])

ylabel('\bf G(x,t)')
xlabel('\bf x-axis')
text( 3.2,0.3 ,'t = 1')
text(-1.1,1.6,'t = 1/36')