Nonstandard Finite Difference Scheme For Singularly Perturbed Parabolic Convection-Diffusion Problems

Abstract

n this thesis, a numerical study is made for solving singularly perturbed time dependent parabolic convection-diffusion problems. To approximate the solution of sin gularly perturbed parabolic convection-diffusion problems, we use nonstandard finite difference method for spatial discretization and Runge kutta Fehlberg method of 4 th and 5 thorder for time discretization. The method is shown to be accurate of order one. A convergence analysis has been carried out to show ε- uniform convergence of the pro posed scheme.