Collocation with quadratic and cubic splines

A. K A Khalifa; J. C. Eilbeck

doi:10.1093/imanum/2.1.111

Collocation with quadratic and cubic splines

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the numerical solution of two-point boundary value problems using the collocation method with equally spaced collocation points, and quadratic or cubic splines as the approximating function. Asymptotic bounds on the maximum error show that, in certain cases, the quadratic spline can give higher accuracy by a factor of between two and three, compared with the cubic spline case. Numerical tests support the theoretical results. © 1982 Academic Press Inc. (London) Limited.

Original language	English
Pages (from-to)	111-121
Number of pages	11
Journal	IMA Journal of Numerical Analysis
Volume	2
Issue number	1
DOIs	https://doi.org/10.1093/imanum/2.1.111
Publication status	Published - Jan 1982

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10.1093/imanum/2.1.111

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title = "Collocation with quadratic and cubic splines",

abstract = "We consider the numerical solution of two-point boundary value problems using the collocation method with equally spaced collocation points, and quadratic or cubic splines as the approximating function. Asymptotic bounds on the maximum error show that, in certain cases, the quadratic spline can give higher accuracy by a factor of between two and three, compared with the cubic spline case. Numerical tests support the theoretical results. {\textcopyright} 1982 Academic Press Inc. (London) Limited.",

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AB - We consider the numerical solution of two-point boundary value problems using the collocation method with equally spaced collocation points, and quadratic or cubic splines as the approximating function. Asymptotic bounds on the maximum error show that, in certain cases, the quadratic spline can give higher accuracy by a factor of between two and three, compared with the cubic spline case. Numerical tests support the theoretical results. © 1982 Academic Press Inc. (London) Limited.

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DO - 10.1093/imanum/2.1.111

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JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

SN - 0272-4979

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Collocation with quadratic and cubic splines

Abstract

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