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pdepe help! (boundry condition in PDE solver)
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Hello, I need some help with differential equation solving in MATLAB.
I need to slove heat-conduction equation: Cρ*dT(x,t)/dt = df(dT(x,t)/dx)/dx.
Boundry condition: T(x,0)=T0; dT(L,t)/dx=0; T(0,t) = Tg(t) [is the upper boundary condition and, (here, Tg is an instrument-recorded temperature)]
However, the boundary conditions Tg(t) are not periodic(Temperature is changed with time and have no fixed transform relation with time).
How can use pdepe to solve it?
Can someone help me??
This is my code:
Josh Meyer on 15 Feb 2019
Your boundary condition function includes the line
pl = ul-TT(i);
TT(i) is not defined within view of the function, so that is what is causing the error. To make that work you need to pass TT in as an extra parameter. But, still, the index i is undefined. So I would recommend just doing something like:
function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t)
Tg = 25; % Or Tg = h(t) if you can express it as a function of t
pl = ul-Tg;
ql = 0;
pr = 0;
qr = 1;
If you really want to pass in TT as a parameter, change the header of the boundary function to
function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t,TT)
and then define the variable
bc = @(xl,ul,xr,ur,t) pdex1bc(xl,ul,xr,ur,t,TT);
This allows pdepe to pass in the 4 inputs it expects, and allows you to pass in the extra TT input from the workspace. You'll need to define the index i somewhere within pdex1bc as well. The call to pdepe then becomes
sol = pdepe(m,@pdex1pde,@pdex1ic,bc,x,t);
Also, although these don't cause errors some other possible issues are: