A computational method for solving quasilinear singular perturbation problems

A class of quasilinear, singularly-perturbed, two-point, boundary value problems for second-order, ordinary differential equations without interior turning points is considered. To solve these problems Newton's method of quasilinearization is adopted. Then the resultant linear problems are solved by the numerical method suggested in [1]. The method presented in [1] is a combination of an exponentially-fitted finite difference method and a classical numerical method. Further, it is based on the boundary value technique [2] generally used to solve singularly-perturbed boundary value problems. Error estimates for the numerical solution of linear problems are stated. Some examples are given to illustrate the method.

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