Computational treatment of a convection-diffusion type nonlinear system of singularly perturbed differential equations

	Computational treatment of a convection-diffusion type nonlinear system of singularly perturbed differential equations
Journal of Mathematical Modeling
مقاله 4، دوره 12، شماره 2، مهر 2024، صفحه 235-246 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

آمار تعداد مشاهده مقاله: 217 تعداد دریافت فایل اصل مقاله: 253

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