Collocation with quadratic and cubic splines

A. K A Khalifa, J. C. Eilbeck

Research output: Contribution to journal › Article

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 languageEnglish
Pages (from-to)111-121
Number of pages11
JournalIMA Journal of Numerical Analysis
Volume2
Issue number1
DOIs
Publication statusPublished - Jan 1982

Fingerprint

Quadratic Spline
Cubic Spline
Collocation
Two-point Boundary Value Problem
Collocation Method
High Accuracy
Numerical Solution

Cite this

Khalifa, A. K A ; Eilbeck, J. C. / Collocation with quadratic and cubic splines. In: IMA Journal of Numerical Analysis. 1982 ; Vol. 2, No. 1. pp. 111-121.
@article{9869489743c64adb9af144171311098f,
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. {\circledC} 1982 Academic Press Inc. (London) Limited.",
author = "Khalifa, {A. K A} and Eilbeck, {J. C.}",
year = "1982",
month = "1",
doi = "10.1093/imanum/2.1.111",
language = "English",
volume = "2",
pages = "111--121",
journal = "IMA Journal of Numerical Analysis",
issn = "0272-4979",
publisher = "Oxford University Press",
number = "1",

}

Khalifa, AKA & Eilbeck, JC 1982, 'Collocation with quadratic and cubic splines', IMA Journal of Numerical Analysis, vol. 2, no. 1, pp. 111-121. https://doi.org/10.1093/imanum/2.1.111

Collocation with quadratic and cubic splines. / Khalifa, A. K A; Eilbeck, J. C.

In: IMA Journal of Numerical Analysis, Vol. 2, No. 1, 01.1982, p. 111-121.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Collocation with quadratic and cubic splines

AU - Khalifa, A. K A

AU - Eilbeck, J. C.

PY - 1982/1

Y1 - 1982/1

N2 - 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.

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.

U2 - 10.1093/imanum/2.1.111

DO - 10.1093/imanum/2.1.111

M3 - Article

VL - 2

SP - 111

EP - 121

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

SN - 0272-4979

IS - 1

ER -

Khalifa AKA, Eilbeck JC. Collocation with quadratic and cubic splines. IMA Journal of Numerical Analysis. 1982 Jan;2(1):111-121. https://doi.org/10.1093/imanum/2.1.111

Access to Document