Generation of pseudospectral differentiation matrices I

Bruno Welfert

doi:10.1137/S0036142993295545

Generation of pseudospectral differentiation matrices I

Bruno Welfert

Research output: Contribution to journal › Article › peer-review

85 Scopus citations

Abstract

We present a simple method for computing n × n pseudospectral differentiation matrices of order p in script type O:(pn²) operations for the case of quasi-polynomial approximation. The algorithm is based on Fornberg's finite difference algorithm and is numerically stable. A Fortran implementation is included. A necessary and sufficient condition for D_p = D₁^p is also given.

Original language	English (US)
Pages (from-to)	1640-1657
Number of pages	18
Journal	SIAM Journal on Numerical Analysis
Volume	34
Issue number	4
DOIs	https://doi.org/10.1137/S0036142993295545
State	Published - 1997

Keywords

Collocation polynomials
Pseudospectral methods

ASJC Scopus subject areas

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1137/S0036142993295545

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abstract = "We present a simple method for computing n × n pseudospectral differentiation matrices of order p in script type O:(pn2) operations for the case of quasi-polynomial approximation. The algorithm is based on Fornberg's finite difference algorithm and is numerically stable. A Fortran implementation is included. A necessary and sufficient condition for Dp = D1p is also given.",

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year = "1997",

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T1 - Generation of pseudospectral differentiation matrices I

AU - Welfert, Bruno

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AB - We present a simple method for computing n × n pseudospectral differentiation matrices of order p in script type O:(pn2) operations for the case of quasi-polynomial approximation. The algorithm is based on Fornberg's finite difference algorithm and is numerically stable. A Fortran implementation is included. A necessary and sufficient condition for Dp = D1p is also given.

KW - Collocation polynomials

KW - Pseudospectral methods

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DO - 10.1137/S0036142993295545

M3 - Article

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JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 4

ER -

Generation of pseudospectral differentiation matrices I

Abstract

Keywords

ASJC Scopus subject areas

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