Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations

Moshe Israeli; Marius Ungarish

doi:10.1007/bf01407865

Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations

Moshe Israeli
, Marius Ungarish

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

17 Scopus citations

Abstract

A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems. Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor of εⁿ⁺¹ can be obtained (where e{open} is the "small" parameter and n is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.

Original language	English
Pages (from-to)	309-324
Number of pages	16
Journal	Numerische Mathematik
Volume	39
Issue number	3
DOIs	https://doi.org/10.1007/bf01407865
State	Published - Oct 1982
Externally published	Yes

Keywords

Subject Classifications: AMS (MOS): 65L10, CR: 5.17

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10.1007/bf01407865

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N2 - A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems. Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor of εn+1 can be obtained (where e{open} is the "small" parameter and n is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.

AB - A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems. Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor of εn+1 can be obtained (where e{open} is the "small" parameter and n is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.

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ER -

Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations

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Keywords

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