Numerical Analysis of a High-Order Scheme for Space-Time Fractional Diffusion-Wave Equations with Riesz Derivatives

Anant Pratap Singh, Higinio Ramos () and Vineet Kumar Singh
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Anant Pratap Singh: Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221005, Uttar Pradesh, India
Higinio Ramos: Department of Applied Mathematics, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
Vineet Kumar Singh: Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221005, Uttar Pradesh, India

Mathematics, 2025, vol. 13, issue 21, 1-18

Abstract: In this paper, we study a class of time–space fractional partial differential equations involving Caputo time-fractional derivatives and Riesz space-fractional derivatives. A computational scheme is developed by combining a discrete approximation for the Caputo derivative in time with a modified trapezoidal method (MTM) for the Riesz derivative in space. We establish the stability and convergence of the scheme and provide detailed error analysis. The novelty of this work lies in the construction of an MTM-based spatial discretization that achieves β -order convergence in space and a ( 3 − α ) -order convergence in time, while improving accuracy and efficiency compared to existing methods. Numerical experiments are carried out to validate the theoretical findings, confirm the stability of the proposed algorithm under perturbations, and demonstrate its superiority over a recent scheme from the literature.

Keywords: finite difference method; Caputo fractional derivative; Riesz fractional derivative; super-diffusion space–time fractional model; numerical stability; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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