e - Uniform Numerical Method for Singularly Perturbed 1D Parabolic Convection-Diffusion Problems

Abstract

In this thesis , ε - Uniform Numerical Method for solving Singularly Perturbed 1D Parabolic Convection-Diffusion Problems is developed using non-standard finite difference method with Runge-Kutta method by applying the method of lines procedure. First, discretizing the spatial domain using uniform mesh and applying non-standard finite difference methods for the spatial direction of singularly perturbed 1D parabolic convection-diffusion problem. Then, the given differential equation transformed to system of initial value problems(IVP) which is solved by RungeKutta method of order two and three implicit. To validate the applicability of the proposed method two model examples were considered and solved for different values of perturbation parameter and mesh sizes. Numerical experiments are carried out extensively to support the theoretical results. The stability is analyzed and the present numerical scheme is of first-order convergence.