University of Tabriz Computational Methods for Differential Equations 2345-3982 13 3 2025 07 01 Two-dimensional temporal fractional advection-diffusion problem resolved through the Sinc-Galerkin method 1047 1058 18383 10.22034/cmde.2024.60039.2560 EN Ali Safaei Department of Mathematics, Faculty of Science, University of Maragheh, Box 55136-553, Maragheh, Iran. Amir Hossein Salehi Shayegan Department of Mathematics n, Faculty of Basic Science, Khatam-ol-Anbia (PBU) University, Tehran, Iran. Mohammad Shahriari Department of Mathematics, Faculty of Science, University of Maragheh, Box 55136-553, Maragheh, Iran. Journal Article 2024 01 12 The Sinc-Galerkin method, even for issues spanning infinite and semi-infinite intervals, is known as exponentially fading mistakes and, in certain circumstances, as the optimum 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. https://cmde.tabrizu.ac.ir/article_18383_6799e70d422f9a043c8d3d8c3417579c.pdf