how to solve system of PDEs?

Hello Everyone,

I need to solve a system of PDEs as follows.

Eq1:

Eq2:

where i=1:10. In other words, they are known functions of x and y.

M and N are unknown functions of x and y.

I would appreciate it if you could help me with solving this system of PDEs.

Thank you!

[Torsten]

In this generality, no advice can be given.

You will have to be more specific about the F_i, the boundary conditions and the domain of integration.

Where do the equations stem from ? Isn't there a literature link where a solution method is suggested ?

[Shahrzad Daghighi]

@Torsten thank you for your answer.

are trigonometric functions.

The domain is described by x and y where both vary from 0 to 90.

Equations represent the governing equation for a structural problem. Unfortunately, for this specific expression, there is not any literature.

I'm not sure how to choose the boundary conditions.

More precisely, how many BCs are needed to solve this system of PDE? Can I use the BCs on both unknown functons (M and N) and their first derivatives ()?

Thank you very much for your time.

[Torsten]

Study CLAWPACK available here:

https://www.clawpack.org/

This package is especially suited to solve hyperbolic PDEs like the one you defined above.

Answer 1

[Bhavana Ravirala]

Refer the below documentation which help you in solving the PDE’s

Solve System of PDEs - MATLAB & Simulink (mathworks.com)

Hope this helps!!

[Torsten]

There is no second-order derivative in both equations. Thus your link doesn't help in this case.