# Questions tagged [finite-difference]

Referring to the discretization of derivatives by Finite differences, and its applications to numerical solutions of partial differential equations.

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### FDTD boundary condition that replicates an infinitely thin mirror

I'm currently running a 1-D FDTD simulation where I want to model a dielectric mirror (with an anti-reflection coating on one side but let's keep it simple for now). For my purposes, the mirror can be ...
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### Prof A. Stanoyevitch's finite difference based PDE matlab code

Where can one find Prof A. Stanoyevitch's finite difference based PDE matlab code? They have a book on such a topic but can't find the accompanying code. Is it well received? It's not commonly talked ...
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### Upwind scheme flux conservation not satisfied in 2D

I have read that the upwind scheme is flux conservative. Then by my understanding, in the absence of sinks/sources and with absorbing boundaries, the amount of the quantity leaving through the ...
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### How to evaluate the points near/at the boundary when using Richardson extrapolation for improved accuracy of a derivative

If we want to improve the accuracy of our numerical estimation of a derivative, we can use Richardson extrapolation. The method is very beneficial when using a centered difference scheme and the ...
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### Can the Runge-Kuta algorithm help in reducing numerical dispersion and anisotropy when using the FDM to solve the 2D wave equation? [closed]

I am currently studying the effects of group velocity on the finite difference solution of the wave equation. Most of what I learned is from this source. I understand that high frequency components in ...
1 vote
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### Reference request: graph Laplacian approximation for domains/manifolds

Is there any reference on solving the heat equation on irregular geometries via creating a mesh and using the graph Laplacian instead of FEM techniques? (Convergence to real solution). That is to say, ...
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### Can I reduce my simulation error with a staggered grid, postprocessing and compatibility equation feedback?

What I did Using the finite difference method, I solved with a certain amount of error the following system of hyperbolic partial differential equations in cylindrical coordinates (the problem is ...
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