On the numerical solution of two‐point boundary value problems

Leslie 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 - 1991

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Insensitivity
Boundary value problems
Integral equations
Integral Equations
Boundary Value Problem
Numerical Solution
High-order Schemes
Order of Convergence
Condition number
Computational efficiency
Discrete Systems
Ordinary differential equations
Computational Efficiency
Boundary Layer
Numerical methods
Finite Difference
Boundary layers
Ordinary differential equation
Differential equations
Finite Element Method

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On the numerical solution of two‐point boundary value problems. / Greengard, Leslie; Rokhlin, V.

In: Communications on Pure and Applied Mathematics, Vol. 44, No. 4, 1991, p. 419-452.

Research output: Contribution to journalArticle

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