NUMERICAL METHODS AND ERROR ESTIMATES FOR A SINGULAR BOUNDARY‐VALUE PROBLEM | Zendy

Pedro M. Lima | Zendy; A. M. Oliveira | Zendy

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NUMERICAL METHODS AND ERROR ESTIMATES FOR A SINGULAR BOUNDARY‐VALUE PROBLEM

Author(s) -

Pedro M. Lima,

A. M. Oliveira

Publication year - 2002

Publication title -

mathematical modelling and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.491

H-Index - 25

eISSN - 1648-3510

pISSN - 1392-6292

DOI - 10.3846/13926292.2002.9637199

Subject(s) - mathematics , discretization , boundary value problem , mathematical analysis , function (biology) , numerical analysis , class (philosophy) , boundary (topology) , discretization error , artificial intelligence , evolutionary biology , computer science , biology

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.

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