Numerical patching method for singularly perturbed two-point boundary value problems using cubic splines

Abstract

A numerical patching method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. The method is distinguished by the following fact: The original singularly perturbed two-point boundary value problem is divided into two problems, namely inner and outer region problems. The terminal boundary condition is obtained from the solution of the reduced problem. Using general stretching transformation, a modified inner region problem is constructed. Then, both inner region problem and outer region problems are solved as two-point boundary value problems by employing cubic splines. Several linear and non-linear problems are solved to demonstrate the applicability of the method.