A higher-order finite difference method for two-dimensional singularly perturbed reaction-diffusion with source-term-discontinuous problem. (15th July 2022)

• Record Type: Journal Article
• Authors: K, Aarthika; Shiromani, Ram; Shanthi, V.
• Is Part Of: Computers & mathematics with applications. Volume 118(2022)
• Page Start: 56
• Page End: 73
• Publication Date: 2022-07-15
• Subjects: Source term discontinuous -- Hybrid scheme -- Shishkin approach -- Singular perturbation -- Elliptic equation -- Two dimensional spaces; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.04.016
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper considers a two-dimensional singularly perturbed reaction-diffusion equation with a discontinuous source term. Due to this discontinuity, interior, corner, and boundary layers appear in the solution for adequately small values of the perturbation parameter ϵ . To achieve a decent estimate of the solution, we construct a numerical approach adopting an efficient hybrid finite difference method that includes a proper layer adapted piece-wise uniform Shishkin mesh. Further, we prove that the hybrid finite difference method is almost second-order uniformly convergent with respect to the perturbation parameter. We have implemented our method to test examples. Numerical results are verifying the theoretical results.