Solving differential equation using ode45

looking to solve this problem using the function ode45

[Torsten]

What are mu, mut, V, h, xi, u ? Your problem statement is much too weird to be answered.

[Greg Zozuls]

This was the problem provided

[Torsten]

And do you understand what you are supposed to do ?

I have the feeling that mu/mut means d/dt and mu^2/Vx^2 means d^2/dx^2.

But what are h(xi) and u(t) ? These functions must be defined somewhere in your assignment.

When you have found them, I suggest you start solving your equation with MATLAB's "pdepe" (at least to get a reference solution).

[Greg Zozuls]

No I don't understand what I'm supposed to do.

u(t) =1 and h(x) = 0.1 if , 0.4 <= x <= 0.6 and h(x)=0 otherwise

thanks

[Torsten]

And what are the x-coordinates of the left and right end of the rod ?

[Greg Zozuls]

0<x<1

Answer 1

[Torsten]

Here is the solution of your problem for reference:

x = linspace(0,1,25);
t = linspace(0,2.5,25);
m = 0;
sol = pdepe(m,@heatcyl,@heatic,@heatbc,x,t);
u = sol(:,:,1);
plot(x,[u(5,:);u(10,:);u(20,:);u(25,:)])

function [c,f,s] = heatcyl(x,t,u,dudx)
u = @(t) 1;
h = @(x) 0.1*(x >=0.4 & x <= 0.6);
c = 1;
f = dudx;
s = h(x)*u(t);
end
%----------------------------------------------
function u0 = heatic(x)
u0 = 0;
end
%----------------------------------------------
function [pl,ql,pr,qr] = heatbc(xl,ul,xr,ur,t)
pl = ul; %ignored by solver since m=1
ql = 0; %ignored by solver since m=1
pr = 0;
qr = 1; 
end
%----------------------------------------------