Two-dimensional temporal fractional advection-diffusion problem resolved through the Sinc-Galerkin method

Document Type : Research Paper

Authors

1 1. Department of Mathematics, Faculty of Science, University of Maragheh, Box 55136-553, Maragheh, Iran. 2. Department of Mathematics n, Faculty of Basic Science, Khatam-ol-Anbia (PBU) University, Tehran, Iran.

2 Department of Mathematics n, Faculty of Basic Science, Khatam-ol-Anbia (PBU) University, Tehran, Iran.

3 Department of Mathematics, Faculty of Science, University of Maragheh, Box 55136-553, Maragheh, Iran.

Abstract

Applying the Sinc-Galerkin method, even for problems that include infinity and semi-infinite intervals, is known as exponential fading errors and in certain conditions as the optimal convergence rate.
Additionally, this approach does not suffer from the normal instability issues that often arise in other methods. Therefore, a numerical technique based on the Sinc-Galerkin method is devised in this study to solve the two-dimensional time fractional advection-diffusion problem. To be precise, the spatial and temporal discretizations of the Sinc-Galerkin and finite difference methods are coupled to provide the suggested approach. Additionally, the suggested method's convergence is looked at. Two numerical examples are provided in depth in the conclusion to demonstrate the effectiveness and precision of the suggested approach.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 26 August 2024

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History

  • Receive Date: 12 January 2024
  • Revise Date: 12 August 2024
  • Accept Date: 21 August 2024

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