An Uniform and Optimal Numerical method to solve Singular Perturbed second order initial value problem

Abstract

This article presents a uniform and optimal numerical method to solve the Singular Perturbed second order initial value problem which occurs in fluid dynamics, and blood flow. The numerical solution of the proposed method in this article reflects the asymptotic behavior of the solution of the given initial value problem. This method works well for small values of the singular perturbation parameter and even for large step sizes. It is a uniform and optimal numerical method. The rate of the order of convergence of the method is proved to be O(min(h, ε)). To view the initial layer the fitted mesh is applied which involves non-uniform mesh. The numerical and graphical results show the performance of the numerical method. In the future, this work will be extended to nonlinear problems and partial differential equations.