Fast Fourier transform method for partial differential equations, case study: The 2-D diffusion equation
type: Item
instance of: scholarly article
title: Fast Fourier transform method for partial differential equations, case study: The 2-D diffusion equation
zbMATH Open document ID: 0656.65098
DOI: 10.1016/0898-1221(88)90182-4
publication date: 1988-01-01T00:00:00Z
review text: The authors consider the 2D constant coefficient diffusion equation in a rectangle (say with first kind boundary conditions). They develop the idea to apply the fast Fourier transform (FFT) in x and y direction to the initial data, to multiply by the n-th power (if the solution at n t is desired) of the transfer function and once more to use FFT to get the numerical result. The arguments in favour of this process are: it does not depend on n (in the sense that the mentioned n-th power can be calculated through exponentials) and hence the solution at n t can be obtained in one step; the difference between explicit and implicit schemes disappears (and the highest order method may be selected; all single parts of this process (FFT, vector multiply) are executable by corresponding hardware. Some timing results of experiments using such equipment are cited.
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65T40
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 4072310
zbMATH Keywords: case study
zbMATH Keywords: finite difference schemes
zbMATH Keywords: linear filter
zbMATH Keywords: diffusion equation
zbMATH Keywords: fast Fourier transform
Wikidata QID: Q115362916
author: Dale H. Mugler
author: Richard A. Scott
reviewed by: Gisbert Stoyan
MaRDI profile type: Publication
full work available at URL: 0898-1221(88)90182-4
OpenAlex ID: W2066925429
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4072310