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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025313 |
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| Summary: | 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. |
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| ISSN: | 2473-6988 |