On the numerical solution of two‐point boundary value problems

L. Greengard, V. Rokhlin

Research output: Contribution to journalArticle

Abstract

In this paper, we present a new numerical method for the solution of linear two‐point boundary value problems of ordinary differential equations. After reducing the differential equation to a second kind integral equation, we discretize the latter via a high order Nyström scheme. A somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using O (N·p2) operations, where N is the number of nodes on the interval and p is the desired order of convergence. Thus, the advantages of the integral equation formulation (small condition number, insensitivity to boundary layers, insensitivity to end‐point singularities, etc.) are retained, while achieving a computational efficiency previously available only to finite difference or finite element methods.

Original languageEnglish (US)
Pages (from-to)419-452
Number of pages34
JournalCommunications on Pure and Applied Mathematics
Volume44
Issue number4
DOIs
StatePublished - Jun 1991

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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