Von Neumann stability analysis

[mattysett13]

Dear all,
I am a new member of this forum. I saw it many and I found it very interesting.

I am solving a 2d transport equation. I discretized it in space with an upwind scheme and in time with Backward Euler difference. Hence, if I want to solve the problem I have to solve a linear system of equation. I have to do it with Gauss-Seidel method.

My question is: I would like to do the Von Neumann Stability analysis of the Gauss-Seidel method but I do not know if it is possible to do it. Anyone can help me, please?

Thank you very much in advance!

Best Regards,
M

 

[jvicens]

aggie

Dear Maggie,

Welcome to the forum! It's great to have a new member who is interested in the field of transport equations. To answer your question, yes, it is possible to perform a Von Neumann Stability analysis on the Gauss-Seidel method. In fact, it is a commonly used technique for analyzing the stability and convergence of numerical methods for solving partial differential equations.

To perform the analysis, you will need to consider the iteration matrix of the Gauss-Seidel method, which is derived from the discretized system of equations. From there, you can apply the Von Neumann Stability criterion, which states that for a numerical method to be stable, the spectral radius of the iteration matrix must be less than or equal to 1.

There are many resources available online that explain the steps for conducting a Von Neumann Stability analysis on different numerical methods, including the Gauss-Seidel method. I would suggest looking into those resources and also consulting with your colleagues or supervisor for guidance.

Best of luck with your analysis and solving the transport equation!