Open AccessNUMERICAL METHODS AND ERROR ESTIMATES FOR A SINGULAR BOUNDARY‐VALUE PROBLEM
Author(s) -
Pedro M. Lima,
Ana Patrícia Oliveira
Publication year - 2002
Publication title -
mathematical modelling and analysis/mathematical modeling 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.