%0 Journal Article
%T A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation
%J Computational Methods for Differential Equations
%I University of Tabriz
%Z 2345-3982
%A Sahu, Subal Ranjan
%A Mohapatra, Jugal
%A Govindarao, Lolugu
%D 2023
%\ 07/01/2023
%V 11
%N 4
%P 822-833
%! A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation
%K Singular perturbation
%K mixed problem
%K Bakhvalov-Shishkin mesh
%K Hybrid scheme
%K uniform convergence
%R 10.22034/cmde.2023.52094.2178
%X A class of singularly perturbed mixed type boundary value problems is considered here in this work. The domain is partitioned into two subdomains. Convection-diffusion and reaction-diffusion problems are posed on the first and second subdomain, respectively. To approximate the problem, a hybrid scheme which consists of a second-order central difference scheme and a midpoint upwind scheme is constructed on Shishkin-type meshes. We have shown that the proposed scheme is second-order convergent in the maximum norm which is independent of the perturbation parameter. Numerical results are illustrated to support the theoretical findings.
%U https://cmde.tabrizu.ac.ir/article_16071_07e7d00f6439054ecf01ce7711824570.pdf