Error in Thomas algorithm

[ptc-5376358]

Hey guys,

I was given a parabolic differential equation with the boundary condition of dT/dR = 0 when R = 0 but I am not quite sure how I am suppose to incorporate that into my Thomas algorithm/Crank-Nicolson program.

I currently have it in the program as u1 = du/dr but it tells me the value must be scalar. When I just get rid of it, there are complex answers in my solution.

Please help?

[AndyWesterman]

HI Emilia,

First step of creating the PDE solution from the differential equations isn't too difficult.

Only issue is that there appears to be a singularity , to avoid this I've added a 10^-299 term in the first equation (keeps MathCad running).

Since you are using a du/dr term in the program later , the U.r() helper function has also been created.

Understanding of what the program is trying to achieve is a little harder.

The indices of the matrices & loops are quite confusing.

Can you explain the basic principles ?

Regards

Andy

[AndyWesterman]

Ok, so never trust the result without a 'sanity check'.

There does seem to be a problem with the initial condition & boundary condition

u(r,0)=0 & u(1,z)=1

at the point r=1,z=0

Need clarification here.

Otherwise the equations have been re-written & seem (now) to work a little better.

Last iteration there were major discrepancies in the A() & B() results.

Regards

Andy

[AlanStevens]

They seem to work even better when expressed as in the attached (though I'm not sure this is any help in sorting out the problems in the Thomas and Crank-Nicholson method!).

Alan