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^*

^*此作品的通讯作者

数学科学学院

Shanghai Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	253-269
页数	17
期刊	Applied Numerical Mathematics
卷	57
期	3
DOI	https://doi.org/10.1016/j.apnum.2006.02.009
出版状态	已出版 - 3月 2007

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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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N2 - 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.

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

UR - https://www.scopus.com/pages/publications/33846794751

U2 - 10.1016/j.apnum.2006.02.009

DO - 10.1016/j.apnum.2006.02.009

M3 - 文章

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VL - 57

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JO - Applied Numerical Mathematics

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

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