Higher order Stable Central Difference with Richardson Extrapolation Method for Second Order Self-Adjoint Singularly Perturbed Boundary Value Problems

Abstract

In this thesis, higher order stable central difference scheme with Richardson extrapolation method have been presented for solving second order self-adjoint singularly perturbed boundary value problems. First, the derivatives of the differential equation are transformed into finite difference approximations that make linear system of algebraic equations in the form of a three-term recurrence relation. Secondly, applying Richardson extrapolation method and then solve by Thomas algorithm. Thirdly, investigate the consistency and stability that guarantees convergence of the proposed method very well. Then, the applicability of the proposed method is validated by implementing it with two model examples and the present method is compared with other methods reported in the literature and exact solution. Finally, maximum absolute error for each model example was shown both by tables and graphs with different perturbation parameters and mesh sizes which shows the betterment of the present method.