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Singh, Richa, Singh, Anshima, Kumar, Sunil, Vigo-Aguiar, Jesus. (1405). A novel high-order approximation method for higher-dimensional time-fractional reaction-diffusion problems with weak initial singularity. سامانه مدیریت نشریات علمی, 14(3), 1040-1067. doi: 10.22034/cmde.2025.61994.2712
Richa Singh; Anshima Singh; Sunil Kumar; Jesus Vigo-Aguiar. "A novel high-order approximation method for higher-dimensional time-fractional reaction-diffusion problems with weak initial singularity". سامانه مدیریت نشریات علمی, 14, 3, 1405, 1040-1067. doi: 10.22034/cmde.2025.61994.2712
Singh, Richa, Singh, Anshima, Kumar, Sunil, Vigo-Aguiar, Jesus. (1405). 'A novel high-order approximation method for higher-dimensional time-fractional reaction-diffusion problems with weak initial singularity', سامانه مدیریت نشریات علمی, 14(3), pp. 1040-1067. doi: 10.22034/cmde.2025.61994.2712
Singh, Richa, Singh, Anshima, Kumar, Sunil, Vigo-Aguiar, Jesus. A novel high-order approximation method for higher-dimensional time-fractional reaction-diffusion problems with weak initial singularity. سامانه مدیریت نشریات علمی, 1405; 14(3): 1040-1067. doi: 10.22034/cmde.2025.61994.2712

A novel high-order approximation method for higher-dimensional time-fractional reaction-diffusion problems with weak initial singularity

Computational Methods for Differential Equations
مقاله 4، دوره 14، شماره 3، مهر 2026، صفحه 1040-1067    اصل مقاله (1.92 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.61994.2712
نویسندگان
Richa Singh1؛ Anshima Singh* 2؛ Sunil Kumar3؛ Jesus Vigo-Aguiar4
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 Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Uttar Pradesh, India.
4Department 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 the Caputo sense. The current approach combines Alikhanov’s L2-1θ 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 covers both stability and convergence, has been provided for one- and two-dimensional problems. Further, to illustrate the accuracy and efficiency of the proposed method, numerical results for two test examples have been presented.
کلیدواژه‌ها
Cubic spline difference scheme؛ Caputo derivative؛ L2-1θ formula؛ Graded mesh؛ ADI scheme؛ Convergence analysis
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