A numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non-smooth source term
The objective of the present paper is to solve a one-dimensional quasilinear parabolic singularly perturbed problem with a discontinuous source term. Due to the presence of such a discontinuity, an interior layer exists at the location of the discontinuity. The problem is solved by discretizing the...
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AIMS Press
2025-03-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025313 |
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| author | Ruby Vembu Shanthi Higinio Ramos |
| author_facet | Ruby Vembu Shanthi Higinio Ramos |
| author_sort | Ruby |
| collection | DOAJ |
| description | The objective of the present paper is to solve a one-dimensional quasilinear parabolic singularly perturbed problem with a discontinuous source term. Due to the presence of such a discontinuity, an interior layer exists at the location of the discontinuity. The problem is solved by discretizing the spatial variable on a piecewise uniform Shishkin mesh using the standard upwind approach, while the backward Euler scheme is employed on a uniform mesh to discretize the time variable. The method is $ \varepsilon $-uniformly convergent, providing first-order convergence in the time domain and almost first-order convergence in the spatial variable. To validate the theoretical findings, the scheme was tested by numerically solving two examples. |
| format | Article |
| id | doaj-art-7c694ad80eff4d018c0c812230e5224e |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj-art-7c694ad80eff4d018c0c812230e5224e2025-08-20T03:16:58ZengAIMS PressAIMS Mathematics2473-69882025-03-011036827685210.3934/math.2025313A numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non-smooth source termRuby0Vembu Shanthi1Higinio Ramos2Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamilnadu, IndiaDepartment of Mathematics, National Institute of Technology, Tiruchirappalli, Tamilnadu, IndiaScientific Computing Group, University of Salamanca, 49029 Zamora, SpainThe objective of the present paper is to solve a one-dimensional quasilinear parabolic singularly perturbed problem with a discontinuous source term. Due to the presence of such a discontinuity, an interior layer exists at the location of the discontinuity. The problem is solved by discretizing the spatial variable on a piecewise uniform Shishkin mesh using the standard upwind approach, while the backward Euler scheme is employed on a uniform mesh to discretize the time variable. The method is $ \varepsilon $-uniformly convergent, providing first-order convergence in the time domain and almost first-order convergence in the spatial variable. To validate the theoretical findings, the scheme was tested by numerically solving two examples.https://www.aimspress.com/article/doi/10.3934/math.2025313convection diffusionquasilinearsingular perturbationshishkin meshstandard upwind schemebackward euler methoddiscontinuous source termweak interior layer |
| spellingShingle | Ruby Vembu Shanthi Higinio Ramos A numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non-smooth source term AIMS Mathematics convection diffusion quasilinear singular perturbation shishkin mesh standard upwind scheme backward euler method discontinuous source term weak interior layer |
| title | A numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non-smooth source term |
| title_full | A numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non-smooth source term |
| title_fullStr | A numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non-smooth source term |
| title_full_unstemmed | A numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non-smooth source term |
| title_short | A numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non-smooth source term |
| title_sort | numerical approach to approximate the solution of a quasilinear singularly perturbed parabolic convection diffusion problem having a non smooth source term |
| topic | convection diffusion quasilinear singular perturbation shishkin mesh standard upwind scheme backward euler method discontinuous source term weak interior layer |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025313 |
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