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# 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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### Orthogonal vs general curvilinear coordinates

Solutions to PDEs over irregular domains can be computed using the finite difference method by the introduction of so called body fitted coordinate systems where the coordinate lines are aligned to ...
3k views

### Laplace's equation problem in Polar Coordinates (Edit)

Is there public code in Matlab for solving the Laplace equation in polar coordinates in a circular domain? I tried a lot but my level of Matlab and Mathematica is not good enough, but still not ...
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### Illustrative examples of mimetic finite difference methods

As much as I try to find a concise explanation on the internet, I can't seem to grasp the concept of a mimetic finite difference, or how it even relates to standard finite differences. It would be ...
12k views

### Recommendation for Finite Difference Method in Scientific Python

For a project I am working on (in hyperbolic PDEs) I would like to get some rough handle on the behavior by looking at some numerics. I am, however, not a very good programmer. Can you recommend ...
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### How should I build a 2D 5-point stencil Laplacian matrix in parallel?

I'm making a simple eigenvalue solver with SLEPc, using a 5-point stencil and the finite difference method. I want to be able to assemble the matrix in parallel. My first thought was just to use <...
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### Optimal transport warping implementation in Matlab

I am implementing the paper "Optimal Mass Transport for Registration and Warping", my goal being to put it online as I just cannot find any eulerian mass transportation code online and this would be ...
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### Implicit finite difference schemes for advection equation

There are numerous FD schemes for the advection equation $\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}=0$ discuss in the web. For instance here: http://farside.ph.utexas.edu/teaching/...
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### What heuristics can be used to minimize the asymptotic matrix bandwidth of a 5-point Laplacian discretization?

I can see that there are multiple heuristics to achieve a matrix with minimum bandwidth. As heuristics, they can't guarantee an optimal solution in polynomial time (after all, the problem is NP-...
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### How to reorder variables to produce a banded matrix of minimum bandwidth?

I'm trying to solve a 2D Poisson equation by finite differences. In the process, I obtain a sparse matrix with only $5$ variables in each equation. For example, if the variables were $U$, then the ...
Suppose I had the following problem: $U_{tt}=U_{xx}+U_{yy}$ in $\Omega=[0,1]\times[0,1]$ $U(x,y,0)=f(x,y)$ $U_{t}(x,y,0)=g(x,y)$ $U=0$ on $\partial \Omega$ I know that there is an explicit ...