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Robust finite difference schemes for one-dimensional parabolic singularly perturbed problems with regular layers | ||
| Computational Methods for Differential Equations | ||
| مقاله 14، دوره 14، شماره 3، مهر 2026، صفحه 1230-1249 اصل مقاله (675.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.63398.2828 | ||
| نویسندگان | ||
| Kishun Kumar Sah* ؛ Subramaniam Gowrisankar | ||
| Department of Mathematics, National Institute of Technology Patna, India. | ||
| چکیده | ||
| In this article, we study the midpoint finite difference scheme for the singularly perturbed parabolic convection diffusion problem on non-uniform meshes, which are determined by a generating function with the boundary layer on the right side of the domain. The non-uniform meshes considered in this work are the classical Shishkin meshes, Shishkin-Bakhvalov meshes, and Shishkin-Bakhvalov modified meshes. Uniform convergence is established with respect to the perturbation parameter on the non-uniform meshes. The backward Euler scheme is applied in the time direction and midpoint finite schemes in the space. Uniform convergence of up to second order in the space and first order in time is obtained. Two numerical examples are considered to validate the numerical and theoretical results obtained. | ||
| کلیدواژهها | ||
| Singularly perturbed parabolic problem؛ Regular boundary layer؛ Midpoint finite difference scheme؛ Shishkin mesh؛ Shishkin-Bakhvalov mesh؛ Shishkin-Bakhvalov modified mesh؛ Generating function؛ Uniform convergence | ||
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