Numerical Treatment of a Two-Parameter Singularly Perturbed Elliptic  Problem with Discontinuous Convection and Source Terms

In this paper, we address a two-parameter singularly perturbed convection-reaction-diffusion 2-D problem. We also consider that the convection and source terms are discontinuous in space. Due to these discontinuities and the presence of perturbation parameters, solutions to such problems show bounda...

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Bibliographic Details
Published inDifferential equations and dynamical systems Vol. 33; no. 1; pp. 303 - 331
Main Authors Shiromani, Ram, Shanthi, Vembu, Ramos, Higinio
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.01.2025
Subjects
Computer Science
Engineering
Mathematics
Mathematics and Statistics
Original Research
65N15
65N12
35J40
35B25
65N06
35J25
Finite difference scheme
Shishkin mesh
Elliptic equation
Two-parameter singularly perturbed problem
65N50
Discontinuous convection and source terms
Two-dimensional space
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Summary:In this paper, we address a two-parameter singularly perturbed convection-reaction-diffusion 2-D problem. We also consider that the convection and source terms are discontinuous in space. Due to these discontinuities and the presence of perturbation parameters, solutions to such problems show boundary and interior layers. In this study, we have carried out a numerical approach using a finite-difference technique with an appropriate layer-adapted piecewise uniform Shishkin mesh. Some examples are presented which show the best performance of the proposed method and its agreement with the theoretical analysis.
ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-024-00676-z