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A robust fitted finite difference method for semi-linear two-parameter singularly perturbed PDEs | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 23 آبان 1404 اصل مقاله (5.36 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.30916.2776 | ||
| نویسندگان | ||
| Mekashaw Ali Mohye* 1؛ Justin B. Munyakazi2؛ Tekle Gemechu Dinka3؛ Yusuf Hussen Haji4؛ Abe NUra Ware4؛ Jemal Muhammed Ahmed5 | ||
| 1Department of Mathematics, College of Natural and Computational Science, Wolkite University, Wolkite, Ethiopia | ||
| 2Department of Mathematics and Applied Mathematics University of Western Cape | ||
| 3Department of Applied Mathematics Adama Science and Technology University | ||
| 4Department of Mathematics, Arsi University, Asela, Ethiopia | ||
| 5Department of Mathematics, Oda Bultum University, Chiro, Ethiopia | ||
| چکیده | ||
| In this article, a new numerical approach is developed for nonlinear two-parameter singularly perturbed initial-boundary value problems. The implicit backward Euler discretization for the time derivative and the fitted operator technique in the spatial domain are employed. Newton's quasilinearization technique is applied to the nonlinear terms. An investigation of parameter-uniform error estimates shows that the developed approach is first-order accurate in both time and space. However, a temporal mesh refinement technique is introduced to improve the order of accuracy to two. Two examples are provided and implemented in Python to validate the applicability of the method, and the results are displayed in tables and graphs. | ||
| کلیدواژه‌ها | ||
| Nonlinear singularly perturbed problems؛ quasilinearization؛ fitted operator finite difference method؛ uniform convergence | ||
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