Numerical algorithm for a general fractional diffusion equation

Rahul Kumar Maurya, Dongxia Li, Anant Pratap Singh and Vineet Kumar Singh

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 223, issue C, 405-432

Abstract: In this manuscript, the analytical solution to the general time fractional diffusion equation followed by the regularity analysis of its solution is presented. Further, a hybrid efficient numerical algorithm for a general fractional derivative of order α∈(0,1) is designed. The physical application of the developed approximation formula is employed to design a hybrid numerical algorithm to determine the numerical solution of the corresponding general time fractional diffusion equation. The proposed numerical techniques are subjected to solvability, numerical stability, and convergence analysis. Numerical example is utilized to verify that (3−α)-th order convergence is attained in time which is higher than the existing scheme (Xu et al., 2013). In the spatial direction, the fourth order convergence is obtained utilizing the compact finite difference method. Besides, such a hybrid numerical algorithm is also used in the stochastic model.

Keywords: Time fractional diffusion model; Regularity; Hybrid difference algorithm; Numerical stability; Convergence analysis (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:223:y:2024:i:c:p:405-432

DOI: 10.1016/j.matcom.2024.04.018

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