A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation

Document Type : Research Paper

Authors

1 Department of Mathematics, Larambha college, Bargarh, Orissa - 768102, India.

2 Department of Mathematics, National Institute of Technology Rourkela, Odisha, India.

3 Department of Mathematics Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore- 641112, India.

Abstract

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.

Keywords

References

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Computational Methods for Differential Equations
Volume 11, Issue 4
July 2023
Pages 822-833

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History

  • Receive Date: 14 June 2022
  • Revise Date: 12 March 2023
  • Accept Date: 03 April 2023

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