Spectral integration and two-point boundary value problems

Research output: Contribution to journalArticle

Abstract

A numerical method for two-point boundary value problems with constant coefficients is developed which is based on integral equations and the spectral integration matrix for Chebyshev nodes. The method is stable, achieves superalgebraic convergence, and requires O(N log N) operations, where N is the number of nodes in the discretization. Although stable spectral methods have been constructed in the past, they have generally been based on reformulating the recurrence relations obtained through spectral differentiation in an attempt to avoid the ill-conditioning introduced by that process.

Original languageEnglish (US)
Pages (from-to)1071-1080
Number of pages10
JournalSIAM Journal on Numerical Analysis
Volume28
Issue number4
StatePublished - Aug 1991

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Two-point Boundary Value Problem
Boundary value problems
Integral equations
Numerical methods
Ill-conditioning
Spectral Methods
Vertex of a graph
Recurrence relation
Chebyshev
Integral Equations
Discretization
Numerical Methods
Coefficient

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Spectral integration and two-point boundary value problems. / Greengard, Leslie.

In: SIAM Journal on Numerical Analysis, Vol. 28, No. 4, 08.1991, p. 1071-1080.

Research output: Contribution to journalArticle

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