Cubic spline method for a class of nonlinear singularly-perturbed boundary-value problems

In this paper, we present a numerical method for solving a class of nonlinear, singularly perturbed two-point boundary-value problems with a boundary layer on the left end of the underlying interval. The original second-order problem is reduced to an asymptotically equivalent first-order problem and is solved by a numerical method using a fourth-order cubic spline in the inner region. The method has been analyzed for convergence and is shown to yield anO(h ⁴) approximation to the solution. Some test examples have been solved to demonstrate the efficiency of the method.The authors thank the referee for his helpful comments.