there are two PDE equations, and boundary&initial condition are known, q is a random noise O(E-3), q0' = 0. y0 = y0' = 0. I want to know what numerical method I can use to solve this PDE.
I‘ve never seen this specific system of PDE but to have an idea of the suitable discretization I first will try to classify mathematically this system. This informatipn is relevant in using the correct numerical BCs, too.
Tou could try to reduce to a set of first order PDE and check the nature of the characteristic curves.
A textbook you could then check about numerical solution of PDE is
https://www.cambridge.org/core/books/numerical-solution-of-partial-differential-equations/EB8E5037C4A49F78D91C0AF7EE4CC7FA#
Filippo Maria Denaro Thanks for your answer. I found a solution in an article, they used finite differential methods to solve this problem. Article Effect of boundary condition and aspect ratio on vortex-indu...
You can use the Finite Difference Method or the Finite Element Method to solve these coupled equations.
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