A second order numerical method for singularly perturbed problem with non-local boundary condition

The aim of this paper is to present a monotone numerical method on uniform mesh for solving singularly perturbed three-point reaction-diffusion boundary value problems. Firstly, properties of the exact solution are analyzed. Difference schemes are established by the method of the integral identities with the appropriate quadrature rules with remainder terms in integral form. It is then proved that the method is second-order uniformly convergent with respect to singular perturbation parameter, in discrete maximum norm. Finally, one numerical example is presented to demonstrate the efficiency of the proposed method.

Automated summary

This paper presents a monotone numerical method for solving singularly perturbed three-point reaction-diffusion boundary value problems on a uniform mesh. The method is proven to be second-order uniformly convergent with respect to the singular perturbation parameter in discrete maximum norm. The efficiency of the proposed method is demonstrated through a numerical example.