Solving Finite Difference BVP with Thomas Algorithm

[all-black]

hye all...

we know that in solving of finite difference methode of boundary value problem, the thomas algorithm is needed to solve it..

anyone here know how to use the thomas algorithm?

thanks.

 

[AlephZero]

The thomas algorithm isn't "needed" to solve finite difference systems.

It is just an optimised algorithm for solving tridiagonal systems of equations. If your FD system produces tridiagonal equations, it might be useful. Otherwise, it's irrelevant.

http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

 

[all-black]

The thomas algorithm isn't "needed" to solve finite difference systems.

It is just an optimised algorithm for solving tridiagonal systems of equations. If your FD system produces tridiagonal equations, it might be useful. Otherwise, it's irrelevant.

http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

yes.. my FD system produces tridiagonal equations..

i use this formula before, but still can't get the answer..

View attachment thomas.pdf

 

[bigfooted]

When you say you can't get the answer, do you mean that you have a particular differential equation with boundary conditions that you're solving using a finite difference scheme and the Thomas algorithm?

If you have implemented the Thomas algorithm yourself, check that it functions properly by using a 3x3 or 4x4 system with a known solution.
If the Thomas algorithm functions as it should, check that you have correctly used the boundary conditions in the system.