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A novel high-order approximation method for higher-dimensional time-fractional reaction-diffusion problems with weak initial singularity | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 15 خرداد 1404 اصل مقاله (2.38 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.61994.2712 | ||
| نویسندگان | ||
| Richa Singh1؛ Anshima Singh* 2؛ Sunil Kumar1؛ Jesus Vigo-Aguiar3 | ||
| 1Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Uttar Pradesh, India. | ||
| 2Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India. | ||
| 3Department of Applied Mathematics, University of Salamanca, Salamanca, Spain. | ||
| چکیده | ||
| The objective of this manuscript is to construct and analyze a fully discrete method to approximate one and two dimensional time-fractional reaction-diffusion equations defined in Caputo sense. The current approach combines Alikhanov’s L2-1$_\theta$ formula on a non-uniform graded mesh to discretize the time-fractional Caputo derivative and the discretization of the space variables using a cubic spline difference scheme. The two-dimensional problem is then separated into two one-dimensional problems using the alternating direction implicit (ADI) approach. The theoretical analysis which consists of both stability and convergence has been provided for both one and two-dimensional problems. Further, in order to illustrate the accuracy and efficiency of the proposed method, numerical results for two test examples have been presented. | ||
| کلیدواژهها | ||
| Cubic splines؛ Caputo derivative؛ Graded mesh, ADI scheme, Convergence analysis | ||
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آمار تعداد مشاهده مقاله: 171 تعداد دریافت فایل اصل مقاله: 279 |
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