High-accuracy fully discrete schemes for 2D time-space fractional models with nonlinear dynamics

Articles in Press

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran.

2 Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA.

Abstract

This paper introduced a fully discrete numerical scheme for solving two-dimensional fractional diffusion equations. The time fractional derivative in the Caputo sense was discretized using a local quadratic polynomial approximation, enhancing accuracy in temporal integration. For spatial fractional derivatives of Riesz type, a nonuniform fractional central difference scheme is developed to effectively handle two-dimensional domains with variable mesh sizes. Stability and convergence analyses confirmed the robustness and precision of the method. Numerical experiments demonstrated that the scheme achieved high-order accuracy in both time and space, validated by exact solutions. The method efficiently managed nonlinear diffusion and reaction terms, showing excellent agreement between numerical and analytical results. Computational performance was evaluated through error norms and CPU time metrics, confirming the methods practical
ity for complex fractional models. This approach offered a flexible and accurate tool for modeling anomalous diffusion processes across various scientific and engineering applications.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 01 January 2025

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History

  • Receive Date: 14 August 2025
  • Revise Date: 08 September 2025
  • Accept Date: 06 October 2025

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