Fourth-order stable central difference method for self-adjoint singular perturbation problems

Abstract

In this paper, fourth order stable central difference method is presented for solving self-adjoint singular perturbation problems for small values of perturbation  parameter, ε . First, the given differential equation was reduced to its conventional form and then it was transformed into linear system of algebraic equations in the form of a three-term recurrence relation, which can easily be solved by using Thomas Algorithm. To validate the applicability of the method, four model examples have been solved for different values of perturbation parameter and mesh sizes. The numerical results are tabulated and compared with some of the previous findings reported in the literature and it is observed that the present method is more efficient. Graphs are also depicted in support of the numerical results. Both theoretical error bounds and numerical rate of  convergence have been established for the method.

Key Words/Phrases: Singular perturbation; stable central difference method;  self-adjoint.