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On the numerical solution of two‐point boundary value problems
Author(s) -
Greengard L.,
Rokhlin V.
Publication year - 1991
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160440403
Subject(s) - mathematics , discretization , boundary value problem , mathematical analysis , gravitational singularity , ordinary differential equation , convergence (economics) , differential equation , interval (graph theory) , finite element method , combinatorics , physics , economics , thermodynamics , economic growth
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 · p 2 ) 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.