Spectral integration and two-point boundary value problems

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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
Issue number4
StatePublished - 1991

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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