A parallel approach for self-adjoint singular perturbation problems using Numerov's scheme

Abstract

In this paper, we considered singularly perturbed self-adjoint boundary-value problems and proposed a computational technique based on Numerov's scheme, which is also suitable for parallel computing. The whole domain is divided into three non-overlapping subdomains, and corresponding subproblems are obtained by using zeroth-order approximations of the solution at the boundaries of these subproblems. The subproblems corresponding to boundary-layer regions are solved using Numerov's method after the introduction of suitable stretching variables and the solution of the reduced problem is taken as an approximate solution in the outer region. A numerical example is provided to show the efficiency and accuracy of the technique.

Keywords:

• Singular perturbation problem
• Boundary layers
• Asymptotic approximation
• Domain decomposition
• Numerov's scheme