آمار
| تعداد نشریات | 45 |
| تعداد شماره‌ها | 1,553 |
| تعداد مقالات | 18,942 |
| تعداد مشاهده مقاله | 63,590,702 |
| تعداد دریافت فایل اصل مقاله | 23,281,542 |
ROBUST NUMERICAL APPROXIMATION FOR A 2D FOURTH-ORDER SINGULARLY PERTURBED ELLIPTIC PROBLEM USING A DECOUPLING STRATEGY | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 29 مهر 1405 اصل مقاله (6.4 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.69545.3430 | ||
| نویسندگان | ||
| Harini Chandrasekaran1؛ Kousalya Ramanujam1؛ Vembu Shanthi1؛ Higinio Ramos Calle* 2 | ||
| 1Department of Mathematics, National Institute of Technology, Tiruchirappalli, 620015, Tamil Nadu, India. | ||
| 21. Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, Salamanca, 37008, Spain. 2. Escuela Polytechnic Superior, Universidad de Salamanca, Campus Viriato, Zamora, 49029, Spain. | ||
| چکیده | ||
| In this work, we study a class of singularly perturbed two-dimensional fourth-order elliptic problems posed on the unit square, which arise in areas such as thin plate theory and fluid dynamics. The numerical approximation of these problems is difficult due to the combined effect of higher-order derivatives and narrow boundary layers. To address these difficulties, the original fourth-order equation is transformed into a system of two second-order equations so that only one equation contains the perturbation parameter ϵ. For the resulting system, we establish a continuous maximum principle together with suitable stability estimates. A finite difference approximation is then developed on a Shishkin mesh to resolve the layer behavior efficiently. The corresponding discrete operator is shown to satisfy the discrete stability properties. In addition, parameter-uniform convergence with almost second-order accuracy is established. The efficiency and uniform performance of the proposed scheme are examined through a collection of numerical experiments carried out for various values of the perturbation parameter. Although the present analysis is carried out for the unit square with smooth coefficients, the approach can be adapted to problems arising in clamped plate models and stream–vorticity formulations of Oseen-type flows. | ||
| کلیدواژه‌ها | ||
| fourth-order elliptic problem؛ singularly perturbed؛ reaction-diffusion type؛ Shishkin mesh؛ finite difference scheme | ||
|
آمار تعداد مشاهده مقاله: 3 تعداد دریافت فایل اصل مقاله: 4 |
||