A computational method for self-adjoint singular perturbation problems using quintic spline

Singularly perturbed self-adjoint boundary-value problems are considered in this article. A difference scheme based on quintic spline is proposed. This scheme is applied to the subproblems obtained from the given problem by dividing the whole domain into nonoverlapping subdomains. The proposed scheme is of fourth-order convergent and more suitable for parallel computers. Stability and convergence of the method are discussed. Numerical examples are provided to show the efficiency and accuracy.