pddd

system of PDE

function pddd

m = 0;

x = [0 0.005 0.01 0.05 0.1 0.2 0.5 0.7 0.9 0.95 0.99 0.995 1];

t = [0 0.005 0.01 0.05 0.1 0.5 1 1.5 2];

sol = pdepe(m,@pdex4pde,@pdex4ic,@pdex4bc,x,t);

u1 = sol(:,:,1);

u2 = sol(:,:,2);

u3 = sol(:,:,3);

figure;

mesh(x,t,u1);

title('U(x,t)');

xlabel('Distance x');

ylabel('Time t');

figure;

mesh(x,t,u2);

title('V(x,t)');

xlabel('Distance x');

ylabel('Time t');

figure;

mesh(x,t,u3);

title('W(x,t)');

xlabel('Distance x');

ylabel('Time t');

% --------------------------------------------------------------------------

function [c,f,s] = pdex4pde(x,t,u,DuDx)

c = [1; 1; 1];

f = [0; 1; 1] .* DuDx;

y = u(1) - u(2)-u(3);

F = exp(5.73*y)-exp(-11.47*y);

s = [-F.*0.5.*u(1); F.*(0.5.*u(2)+1.5); F.*(-0.00.*u(3)+0)];

%f = [0; 1] .* DuDx;

%F=exp(1.*(0.5));

%s=[-F.*2.*u(1);F.*2.*u(2)+0];

% --------------------------------------------------------------------------

function u0 = pdex4ic(x);

u0 = [1;0;0];

% --------------------------------------------------------------------------

function [pl,ql,pr,qr] = pdex4bc(xl,ul,xr,ur,t)

pl = [0; ul(2); ul(3)];

ql = [1; 0; 0];

pr = [ur(1)-1; 0;1];

qr = [0; 1; 1];