A NUMERICAL SCHEME WITH HIGH ACCURACY TO SOLVE THE TWO-DIMENSIONAL TIME-SPACE DIFFUSION-WAVE MODEL IN TERMS OF THE RIEMANN-LIOUVILLE AND RIESZ FRACTIONAL DERIVATIVES

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.

2 Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey.

Abstract

In this paper, we propose a hybrid and efficient numerical scheme with high accuracy to obtain approximate solutions of the two-dimensional time-space diffusion-wave model in terms of the RiemannLiouville and Riesz fractional derivatives. To discretise the presented model, two approaches are used in the directions of space and time. In the time direction, we use a second-order accurate difference numerical method and the weighted shifted Grunwald derivative approximation of second-order. The weighted shifted Gr¨unwald derivative approximation is used to estimate the Riemann–Liouville’s fractional operator. Also, in the space direction, the Galerkin spectral method based on the modified Jacobi functions is used. The study of convergence and stability analysis for the proposed numerical approach is presented. At the end, some numerical examples are given to show the effectiveness of the proposed numerical scheme. For all the examples, graphs are drawn, and numerical results are
reported in tables.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 11 August 2025

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History

  • Receive Date: 24 February 2025
  • Revise Date: 23 May 2025
  • Accept Date: 10 August 2025

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