A computational method for solving singular perturbation problems

摘要

A class of singularly perturbed two point boundary value problems for second order ordinary differential equations is considered. In order to solve them, a computational method is suggested in which exponentially fitted difference schemes are combined with classical numerical methods. The proposed method is distinguished by the following facts: first, we divide the given interval (the domain of definition of differential equation) into two subintervals called inner and outer regions. Then we solve the differential equation over both the regions as two point boundary value problems. The terminal boundary condition of the inner region is obtained using the zero-order asymptotic expansion of the solution. Some numerical examples are given to illustrate the method.