2nd order ODE dependent on two variables (t and x)

Hello,

I am trying to solve the attached second order ODE dependent on two variables.

Could anyone please give me some hints on how to proceed?

Thank you very much.

[Star Strider]

You will likely need the Partial Differential Equation Toolbox for this problem.

[Torsten]

A typical problem for MATLAB's "pdepe".

https://de.mathworks.com/help/matlab/ref/pdepe.html

Answer 1

[SAI SRUJAN]

Hi Ricard Escriva,

I understand that you are trying to solve a non linear partial differential equation.

Typically, the Partial Differential Equations (PDEs) in MATLAB adhere to the following format:

c(x,t,u,du/dx).du/dt=(x^-m).d/dx[(x^-m)f(x,t,u,du/dx)]+s(x,t,u,du/dx)

Given a PDE, model the partial differential equation to make an analogy to the format specified above.To be more specific in resolving the issue, you can use the "pdepe" MATLAB function to further solve the issue by setting initial and boundary conditions.

For a comprehensive understanding of the "pdepe" function in MATLAB, please refer to the following documentation.

Solve System of PDEs - MATLAB & Simulink - MathWorks India

Solve 1-D parabolic and elliptic PDEs - MATLAB pdepe - MathWorks India