A smart nonstandard finite difference scheme for second order nonlinear boundary value problems

Authors:
Utku Erdogan;Turgut Ozis
Affiliations:
Ege University, Science Faculty, Department of Mathematics, C-01/b, 35100 Bornova-Izmir, Turkey and University of Groningen, Department of Mathematics and Computing Science, Bernoulliborg 450, Nij ...;Ege University, Science Faculty, Department of Mathematics, C-01/b, 35100 Bornova-Izmir, Turkey
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

A new kind of finite difference scheme is presented for special second order nonlinear two point boundary value problems. An artificial parameter is introduced in the scheme. Symbolic computation is proposed for the construction of the scheme. Local truncation error of the method is discussed. Numerical examples are illustrated. Numerical results show that the method is very effective.