An Efficient Computational Algorithm for a Class of Nonlinear Singular Perturbation Problems of Convection Diffusion Type with Cauchy Data

This article aims at the construction and analysis of a computational method for a class of singularly perturbed nonlinear differential equations of convection diffusion type with Cauchy data. A computational method, which is a combination of finite difference operators and a Shishkin mesh, is constructed to solve the class of problems. An algorithm involving the continuation technique together with the suggested computational method is developed to solve the class of problems numerically. The newly developed computational method is proved to be essentially first-order parameter-independent convergent. Computational experiments included support the theoretical results.