PDEPE and BCFUN

Hello,

I would like to use pdepe for solving Heat equation in 1D with a non linear coefficient. I know it is possible. But I remain stuck with the boundary condition and pl,pr,ql,qr.

Let us consider a classic Heat equation : pi^2 dUdt = d2U/dx2 with, U(0,x)= sin(pi x) and as boundary condition : u(t,0)=0=u(t,1) for t>=0 and 0<=x<=1

How do you translate this boundary condition into BCfun and pl,pr,qr,ql ??

Thanks. Alex.

Answer 1

[Grzegorz Knor]

Below is the full code:

function heat1D

m = 0;
xmesh = linspace(0,1,20);
tspan = linspace(0,3,60);

sol = pdepe(m,@pdefunH,@icfunH,@bcfunH,xmesh,tspan);

u = sol(:,:,1);
surf(xmesh,tspan,u)

function [c,f,s] = pdefunH(x,t,u,dudx)
c = pi^2;
f = dudx;
s = 0;

function u = icfunH(x)
u = sin(pi*x);

function [pl,ql,pr,qr] = bcfunH(xl,ul,xr,ur,t)
pl = ul;
ql = 0;
pr = ur;
qr = 0;

[HARRISON WANDERA]

@Grzegorz Knor how will the boundary conditions look like for the same equation but in two dimension case?

[HARRISON WANDERA]

@Grzegorz Knor i wrote them this way:

pl = [ul(1);ul(2)];

ql = [0;0];

pr = [ur(1);ur(2)];

qr = [0;0];

but i think am not correct because my code is not running as i expected. I will appreciate your intervention.