A numerical method for solving singularly perturbed systems of nonlinear two-point boundary-value problems

Abstract

In this paper, a numerical method is proposed to solve singularly perturbed systems of nonlinear two-point boundary-value problems. First, Newton's iteration is used to linearize such problems, reducing these to a sequence of linear singularly perturbed two-point boundary-value problems. Then,a difference scheme is applied to solve the linear systems. The difference scheme is accurate up to O(h ²). Test examples are included to demonstrate the efficiency of the method.

Keywords:

• Perturbed system
• Newton iteration
• boundary value problem

C.R. Categories:

• G.1.7
• G.1.5