The extrapolation of Numerov's scheme for nonlinear two-point boundary value problems

Yuan Ming Wang

doi:10.1016/j.apnum.2006.02.009

The extrapolation of Numerov's scheme for nonlinear two-point boundary value problems

Yuan Ming Wang^*

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai Normal University

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

7 Scopus citations

Abstract

This paper is concerned with the extrapolation algorithm of Numerov's scheme for semilinear and strongly nonlinear two-point boundary value problems. The asymptotic error expansion of the solution of Numerov's scheme is obtained. Based on the asymptotic error expansion, Richardson's extrapolation is constructed, and so the accuracy of the numerical solution is greatly increased. Numerical results are presented to demonstrate the efficiency of the extrapolation algorithm.

Original language	English
Pages (from-to)	253-269
Number of pages	17
Journal	Applied Numerical Mathematics
Volume	57
Issue number	3
DOIs	https://doi.org/10.1016/j.apnum.2006.02.009
State	Published - Mar 2007

Keywords

Asymptotic error expansion
Nonlinear two-point boundary value problem
Numerov's method
Richardson's extrapolation

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10.1016/j.apnum.2006.02.009

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title = "The extrapolation of Numerov's scheme for nonlinear two-point boundary value problems",

abstract = "This paper is concerned with the extrapolation algorithm of Numerov's scheme for semilinear and strongly nonlinear two-point boundary value problems. The asymptotic error expansion of the solution of Numerov's scheme is obtained. Based on the asymptotic error expansion, Richardson's extrapolation is constructed, and so the accuracy of the numerical solution is greatly increased. Numerical results are presented to demonstrate the efficiency of the extrapolation algorithm.",

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year = "2007",

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AB - This paper is concerned with the extrapolation algorithm of Numerov's scheme for semilinear and strongly nonlinear two-point boundary value problems. The asymptotic error expansion of the solution of Numerov's scheme is obtained. Based on the asymptotic error expansion, Richardson's extrapolation is constructed, and so the accuracy of the numerical solution is greatly increased. Numerical results are presented to demonstrate the efficiency of the extrapolation algorithm.

KW - Asymptotic error expansion

KW - Nonlinear two-point boundary value problem

KW - Numerov's method

KW - Richardson's extrapolation

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DO - 10.1016/j.apnum.2006.02.009

M3 - 文章

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SP - 253

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JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

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The extrapolation of Numerov's scheme for nonlinear two-point boundary value problems

Abstract

Keywords

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