A sixth order numerical method for a class of nonlinear two-point boundary value problems

Xiao-Yu Zhang; Qing Fang

doi:10.3934/naco.2012.2.31

Article Contents

2012, Volume 2, Issue 1: 31-43. Doi: 10.3934/naco.2012.2.31

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A sixth order numerical method for a class of nonlinear two-point boundary value problems

Xiao-Yu Zhang^1, and
Qing Fang^1,

1.
Department of Mathematical Sciences, Faculty of Science, Yamagata University, Yamagata 990-8560

Received: April 2011

Revised: June 2011

Published: March 2012

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we are concerned with the numerical solution of a class of nonlinear two-point boundary value problems with general boundary conditions. We propose a new numerical method of sixth order accuracy by integrating compact finite difference methods with the Green's function approach. It is the first sixth order accurate numerical scheme on non-uniform grids for the problem. We also give numerical results of some practical problems including reaction-diffusion equations. It is remarked that our numerical method is also efficient for layer equations.

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Mathematics Subject Classification: Primary: 65L10; Secondary: 65L12.

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