How Can TDMA and Gauss-Seidel Line Relaxation Solve a Complex PDE in MATLAB?

[tetirichie]

Hi

Urgent Thanks in advance.

Could somebody who knows how to solve the above mentioned equation please assist.The equation needs to be solved using any language but I am now very comfortable with matlab.

I am trying to solve the following eqaution using TDMA and Gauss-Seidel line relaxation:

$$A\frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} = 0$$

$$A = 1 - M^2_\infty - (\gamma + 1)\frac{M^2_\infty}{u_\infty}\frac{\partial \phi}{\partial x}$$

$$u_\infty = 1 ; M^2_\infty = 0.975 ; \gamma = 1.4$$

My email is teti@myself.com

With Regards,

Richard

 

[arildno]

Are there any problems with an iteration loop on A to handle the non-linearity embedded in it?

 

[M98Ranger]

Hi Richard,

Thank you for reaching out for assistance with solving your partial differential equation. I am not able to solve it for you, but I can provide some guidance and resources that may be helpful.

A partial differential equation (PDE) is an equation that involves multiple independent variables and their partial derivatives. In your case, the equation has two independent variables, x and y, and their second order partial derivatives. PDEs are commonly used in physics, engineering, and other fields to model complex systems and phenomena.

To solve a PDE, there are various numerical methods that can be used, such as finite difference, finite element, and spectral methods. TDMA (Tri-Diagonal Matrix Algorithm) and Gauss-Seidel line relaxation are two specific methods that can be used to solve PDEs numerically. These methods involve breaking down the problem into a system of linear equations and iteratively solving them to approximate the solution to the PDE.

Since you mentioned that you are comfortable with MATLAB, you may find it helpful to use the built-in functions and tools in MATLAB for solving PDEs. MATLAB has a PDE Toolbox that allows you to specify the PDE, boundary conditions, and numerical method, and it will solve the equation for you. There are also many online resources and tutorials available for using MATLAB for PDEs.

I hope this information helps you in solving your equation. If you have any further questions or need clarification, please feel free to reach out. Best of luck with your project!

Regards,