Applications - A Guide to MATLAB for Beginners and Experienced Users - page 195

surf(x,t,u); title(['Numerical solution',...
'computed with 21 mesh points in x.'])

xlabel('x'), ylabel('t'), zlabel('u')
% A solution profile can also be illuminating.
figure
plot(x,u(end,:))
title('Solution att=4')
xlabel('x'), ylabel('u(x,4)')
%----------------------------------------------------------
function [c,f,s] = pdex(x,t,u,DuDx)
c=1;
f = (1 + (x/5).ˆ2)*DuDx;
% flux is variable conductivity times u x
s=0;
% ---------------------------------------------------------
function u0 = pdexic(x)
% initial condition att=0
u0 = 20+5*sign(x);
% ---------------------------------------------------------
function [pl,ql,pr,qr] = pdexbc(xl,ul,xr,ur,t)
% q's are zero since we have Dirichlet conditions
%pl=0attheleft, pr=0attheright endpoint
pl = ul-15;
ql=0;
pr = ur-25;
qr=0;
Running it gives
heateqex2

Numerical solution computed with 21 mesh points in x.

25

20

15

4

3 5

2

0

1

0 -5

t

x