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

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.