A numerical approach for singularly perturbed parabolic reaction-diffusion problem on a modified graded mesh
This paper addresses the numerical approximations of solutions for one dimensional parabolic singularly perturbed problems of reaction-diffusion type. The solution of this class of problems exhibit boundary layers on both sides of the domain. The proposed numerical method involves combining the back...
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| Vydáno v: | Journal of numerical analysis and approximation theory Ročník 54; číslo 1; s. 117 - 139 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Publishing House of the Romanian Academy
30.06.2025
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| Témata: | |
| ISSN: | 2457-6794, 2501-059X |
| On-line přístup: | Získat plný text |
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| Shrnutí: | This paper addresses the numerical approximations of solutions for one dimensional parabolic singularly perturbed problems of reaction-diffusion type. The solution of this class of problems exhibit boundary layers on both sides of the domain. The proposed numerical method involves combining the backward Euler method on a uniform mesh for temporal discretization and an upwind finite difference scheme for spatial discretization on a modified graded mesh. The numerical solutions presented here are calculated using a modified graded mesh and the error bounds are rigorously assessed within the discrete maximum norm. The primary focus of this study is to underscore the crucial importance of utilizing a modified graded mesh to enhance the order of convergence in numerical solutions. The method demonstrates uniform convergence, with first-order accuracy in time and nearly second-order accuracy in space concerning the perturbation parameter. Theoretical findings are supported by numerical results presented in the paper. |
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| ISSN: | 2457-6794 2501-059X |
| DOI: | 10.33993/jnaat541-1513 |