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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Laplacian eigenmodes on a semi-circular region with finite-difference method
The computation of eigenmodes of a semi-circular membrane reduces to the following eigenvalue problem
$$\nabla^2u=k^2u\;,$$
where the region of interest is a semi-circle defined by $r\in[0,1]$ and $\...
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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 ...
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How to obtain an implicit finite difference scheme for the wave equation?
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 ...
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How can I reduce the communication bottleneck of a parallel explicit finite difference scheme?
Suppose i was trying to solve a parabolic PDE (heat equation) on a rectangular domain using an explicit finite difference scheme. I am storing my solution vector in a matrix form (because it closely ...
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Finite differences on domains with irregular boundaries
Can anybody help me to find the books on numerical solutions(finite difference and Crank–Nicolson methods) of Poisson and diffusion equations including examples on irregular geometry, such as a domain ...
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How can I numerically differentiate an unevenly sampled function?
Standard finite difference formulas are usable to numerically compute a derivative under the expectation that you have function values $f(x_k)$ at evenly spaced points, so that $h \equiv x_{k+1} - x_k$...
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