Numerical methods and error estimates for a singular boundary-value problem

Pedro Miguel Lima; António Manuel Morais Fernandes de  Oliveira

doi:10.1080/13926292.2002.9637199

Numerical methods and error estimates for a singular boundary-value problem

Pedro Miguel Lima, António Manuel Morais Fernandes de Oliveira

DM - Departamento de Matemática

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

4 Citations (Scopus)

Abstract

In this paper we analyze a class of equations of the form y? (x) = —g(x) x^p (y(x))^q where p and q are real parameters satisfying p > ^_1, g < ^_1 and g is a positive and continuous function on [0,1]. We search for positive solutions which satisfy the boundary conditions y'(0)=y(l) = 0. Numerical approximations of the solution are obtained by means of a finite difference scheme and the asymptotic expansion of the discretization error is deduced. Some numerical examples are analyzed.

Original language	English
Pages (from-to)	271-284
Number of pages	14
Journal	Mathematical Modelling And Analysis
Volume	7
Issue number	2
DOIs	https://doi.org/10.1080/13926292.2002.9637199
Publication status	Published - 2002

Keywords

Asymptotic expansion
Finite differences scheme
Singular problems

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AB - In this paper we analyze a class of equations of the form y? (x) = —g(x) xp (y(x))q where p and q are real parameters satisfying p > _1, g < _1 and g is a positive and continuous function on [0,1]. We search for positive solutions which satisfy the boundary conditions y'(0)=y(l) = 0. Numerical approximations of the solution are obtained by means of a finite difference scheme and the asymptotic expansion of the discretization error is deduced. Some numerical examples are analyzed.

KW - Asymptotic expansion

KW - Finite differences scheme

KW - Singular problems

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DO - 10.1080/13926292.2002.9637199

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EP - 284

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JF - Mathematical Modelling And Analysis

IS - 2

ER -

Numerical methods and error estimates for a singular boundary-value problem

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Keywords

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