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A fitted mesh method for a coupled system of two singularly perturbed first order differential equations with discontinuous source term | ||
| Journal of Mathematical Modeling | ||
| مقاله 10، دوره 8، شماره 1، خرداد 2020، صفحه 55-70 اصل مقاله (325.16 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2020.12824.1245 | ||
| نویسندگان | ||
| Sheetal Chawla1؛ Urmil Suhag2؛ Jagbir Singh* 2 | ||
| 1Department of Mathematics, Pt. N.R.S. Government College Rohtak, Haryana-124001, India | ||
| 2Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana-124001, India | ||
| چکیده | ||
| In this work, an initial value problem for a weakly coupled system of two singularly perturbed ordinary differential equations with discontinuous source term is considered. In general, the system does not obey the standard maximum principle. The solution to the system has initial and interior layers that overlap and interact. To analyze the behavior of these layers, piecewise-uniform Shishkin meshes and graded Bakhvalov meshes are constructed. A backward finite difference scheme is considered on the meshes and is proved to be uniformly convergent in the maximum norm. Numerical experiments for both the Shishkin and Bakhvalov meshes are provided in support of the theory. | ||
| کلیدواژه‌ها | ||
| Singular perturbation؛ parameter-uniform convergence؛ backward difference scheme؛ Shishkin mesh؛ Bakhvalov mesh؛ initial and interior layers | ||
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