Accelerated Fitted Mesh Finite Difference Method For Singularly Perturbed Self-Ad joint Boundary Value Problem

Abstract

In this thesis, accelerated tted mesh nite di erence method is presented for solving Singularly perturbed Self-adjoint boundary value problems. First, the derivatives of the di erential equation are transformed into nite di erence approximations that make lin ear system of algebraic equations in the form of a three-term recurrence relation which can easily be solved by Thomas algorithm. And then, Richardson extrapolation method is applied to accelerate the convergence. Second, establish the convergence of the pro posed method very well. Finally, validate results using numerical model examples and compared with other methods listed in the literature and exact solution. Maximum absolute error for each model example shown by tables and behavior of graphs with dif ferent perturbation parameters and mesh sizes which shows the betterment of the present method.