Collocation Methods for Singular Boundary Value Problems

The application of collocation methods based on piecewise polynomials to the numerical solution of boundary value problems for systems of ordinary differential equations with a singularity of the first kind is examined. The schemes are shown to be stable and convergent. Enhanced accuracy at the node...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 15; no. 1; pp. 198 - 217
Main Authors De Hoog, Frank R., Weiss, Richard
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.02.1978
Subjects
Approximation
Boundary conditions
Boundary value problems
Cauchy problem
Degrees of polynomials
Eigenvalues
Mathematical extrapolation
Ordinary differential equations
Polynomials
Textual collocation
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Summary:The application of collocation methods based on piecewise polynomials to the numerical solution of boundary value problems for systems of ordinary differential equations with a singularity of the first kind is examined. The schemes are shown to be stable and convergent. Enhanced accuracy at the nodes for suitably chosen collocation points (superconvergence) is established for a class of important problems.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0036-1429
1095-7170
DOI:10.1137/0715013