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Computational treatment of a convection-diffusion type nonlinear system of singularly perturbed differential equations | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 بهمن 1402 اصل مقاله (346.78 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2024.25939.2301 | ||
| نویسنده | ||
| Manikandan Mariappan* | ||
| Department of Mathematics, School of Engineering, Presidency University, Bengaluru - 560 064, Karnataka, India | ||
| چکیده | ||
| In this article, a nonlinear system of singularly perturbed differential equations of convection-diffusion type with Dirichlet boundary conditions is considered on the interval $[0,1].$ Both components of the solution of the system exhibit boundary layers near $t = 0.$ A new computational method involving classical finite difference operators, a piecewise-uniform Shishkin mesh and an algorithm based on the continuation method is developed to compute the numerical approximations. The computational method is proved to be first order convergent uniformly with respect to the perturbation parameters. Numerical experiments support the theoretical results. | ||
| کلیدواژه‌ها | ||
| Nonlinear system of singularly perturbed differential equations؛ boundary layers؛ finite difference scheme؛ Shishkin mesh؛ the continuation method؛ parameter-uniform convergence | ||
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آمار تعداد مشاهده مقاله: 55 تعداد دریافت فایل اصل مقاله: 96 |
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