# Pseudo-spectral method solution for wave equation PDE: d^2p/dt^2=​(c^2)*[d^2​p/dx^2 + d^2p/dy^2 + d^2p/dz^2]

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Hussein Muhammed on 9 May 2022
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).
regards,

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.
HTH
Hussein Muhammed on 9 May 2022
the key step in solving the acoustic wave equation in Riemannian coordinates is that the spatial axes of the laplacian operator have to approximated by Fourier Pseudo-spectral methods, all I need is a working code example of that method for any similer PDE then I can start my code.