Eighth Order Compact Finite Difference Method For Singularly Perturbed One Dimensional Reaction Diffusion Problems

Abstract

In this thesis, eighth order compact finite difference method has been presented for solving singularly perturbed one dimensional reaction diffusion problems. First, the given interval is discretized and the given differential equation is replaced by finite difference approximations. Then, the given differential equation is transformed to linear systems of algebraic equations and then using Taylor’s series and central finite difference approximation, it is reduced to a three term recurrence relation which can be easily solved by using Thomas Algorithm. To validate the applicability of the proposed method three model examples with and without exact solution were considered and solved for different values of perturbation parameter and mesh sizes. Numerical experiments are carried out extensively to support the theoretical results using MATLAB software. The results have beenpresented in tables in terms of maximum absolute errors and also in graphs. Thepresent method approximates the exact solution very well. Both the theoretical and computational rate of convergence has been established and observed to be in agreement.In a net shellthe present method is simple and efficient than some of the methods reported in the literature.