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Solve linear singularly perturbed boundary value problems via domain decomposition and reproducing kernel collocation | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 04 خرداد 1405 اصل مقاله (1.34 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.70289.3481 | ||
| نویسندگان | ||
| X. L. Li؛ Fazhan Geng* | ||
| Department of Mathematics, Suzhou University of Technology, Changshu, Jiangsu 215500, PR China. | ||
| چکیده | ||
| We propose a uniformly convergent numerical scheme for singularly perturbed boundary value problems with a single boundary layer. The method combines the advantages of reproducing kernel theory with a domain decomposition strategy. Without loss of generality, we focus on problems exhibiting a left boundary layer, as the analysis for a right layer is mathematically equivalent. The original problem is first split into a boundary layer problem and a regular problem. The regular part is solved numerically using a high-order reproducing kernel collocation method on a uniform mesh, while the boundary layer part is resolved on a graded mesh using a similar high-order scheme. Both theoretical analysis and numerical experiments confirm the parameter-uniform convergence of the proposed approach. | ||
| کلیدواژه‌ها | ||
| Reproducing kernel؛ convection-diffusion problems؛ boundary layers | ||
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آمار تعداد مشاهده مقاله: 112 تعداد دریافت فایل اصل مقاله: 166 |
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