Accurate Numerical Method For Singularly Perturbed Reaction-Diffusion Equations

Abstract

In this thesis, we considered a time dependent one-dimensional singularly perturbed parabolic reaction-diffusion problems. We proposed a parameter-uniform numerical scheme to solve the problems. First, we dicretized the continuous problem of space variable using a non standard finite difference method via the method of line, then the spatial discretization is transformed to a system of initial value problems. After changing the spatial discretization to initial value problem, the time derivative is solved using second order Fehlberg Runge Kutta method. The method is second order parameter-uniform convergent in both space and time direction.