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

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, Uttar Pradesh, India.

2 Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India.

3 Department of Applied Mathematics, University of Salamanca, Salamanca, Spain.

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 05 June 2025

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History

  • Receive Date: 13 June 2024
  • Revise Date: 19 May 2025
  • Accept Date: 22 May 2025

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