A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation
نویسندگان
1 Department of Mathematics, Larambha college, Bargarh, Orissa - 768102, India.
2 Department of Mathematics Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore- 641112, India.
3 Department of Mathematics, National Institute of Technology Rourkela, Odisha, India.
doi
10.22034/cmde.2023.52094.2178چکیده
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.
