Pseudo-spectral method solution for wave equation PDE: d^2p/dt^2=(c^2)*[d^2p/dx^2 + d^2p/dy^2 + d^2p/dz^2]
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I'm trying to solving above wave equation via Pseudo-spectral method instead of finite-difference scheme, for the sake of solving very complicated type of wave equation called: wave equation in Riemannian coordinate system (https://reproducibility.org/RSF/book/cwp/jse2006RWEImagingOverturningReflections/paper_html/) can seniors please help me y sugesstions and intial MATLAB codes. An initial MATLAB code for solving the wave equation in Cartesian coordinate system can be found here (https://github.com/Jaguar101-jr/1-D-wave-equation-in-Matlab).
Bjorn Gustavsson on 9 May 2022
This is just a linear wave-equation with constant speed of the waves. The general solution is just:
So you just have to determine the complex-valued for all that you need to fit your initial and boundary-conditions. After that you'll have the solution as a number of propagating plane-wave-modes that describe the p-variation. From what you've given us so far it is difficult to give more specific advice.