use of pdepe for a space-dependent diffusivity

I have a space-dependent heat equation

Dc/dt = d/dx (D(x) dc/dx)

where the function D(x) is not defined as a function, but a position-dependent

vector of (n) points : diff

The vector diff has the same length of x, so I have x(i) and diff(i), i=1,…,n

How can I implement pdepe?

cb = pdepe(m,@heatcyl,@heatic,@heatbc,x,t); % run solver

function [c,f,s] = heatcyl(x,t,u,dudx) % diffusion equation equation

c = 1;

f = dudx*diff; ???? <<<<<<<<< not sure about that, since diff is a vector

s = 0;

end

function u0 = heatic(x) % initial condition

u0=1;

end

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

global diff n

pl=0;

ql=1;

pr=ur;

qr=0;

end

Thank you!

Answer 1

[Torsten]

First: Don't name the vector "diff" since "diff" is an internal MATLAB function. Name it D, e.g.

Second: To get the correct value of D, use

f = interp1(X,D,x)*dudx;

where X is the coordinate vector to which the D-values belong.

You can pass both to your function by using

cb = pdepe(m,@(x,t,u,dudx)heatcyl(x,t,u,dudx,X,D),@heatic,@heatbc,x,t); % run solver
...
function [c,f,s] = heatcyl(x,t,u,dudx,X,D) % diffusion equation equation
  c = 1;
  f = interp1(X,D,x)*dudx; 
  s = 0;
end

[Giuseppe Pontrelli]

thank you Torsten. Your suggestions were very useful, and now the code run nicely!