Abstract:
In this thesis, accelerated finite difference method for solving singularly perturbed
boundary value problems with two small parameters is presented. First, the solution domain
is discretized. Then, the derivatives in the given boundary value problem are replaced by finite
difference approximations.The numerical scheme that provides algebraic systems of equations
is obtained. The system can easily be solved by Thomas algorithm. The consistency, stability
and convergence of the method have been established. The established convergence of the
scheme is further accelerated by applying the Richardsons extrapolation which yields sixth
order convergence. To validate the applicability of the proposed method, two model examples
have been considered and solved for different values of perturbation parameters and mesh
sizes. Both theoretical error bounds and numerical rate of convergence have been established
for the method. The numerical results have been presented in tables and graphs to illustrate;
the present method approximates the exact solution very well. Moreover, the present method
gives better results than some of numerical methods mentioned in the literature.
