Novel Computational Methods Based on Shifted Jacobi Operational Matrix for Time-Space Fractional Advection-Dispersion Equation

Shivanian, Elyas; Khodabandehlo, Hamid Reza; Chegini, Tannaz Goodarzvand; Haghighi, Donya

doi:10.22060/ajmc.2025.24428.1420

Novel Computational Methods Based on Shifted Jacobi Operational Matrix for Time-Space Fractional Advection-Dispersion Equation

Articles in Press

Document Type : Original Article

Authors

Elyas Shivanian ¹

Hamid Reza Khodabandehlo ²

Tannaz Goodarzvand Chegini ³

Donya Haghighi ²

¹ Imam Khomeini International University, Qazvin, IRAN

² Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34148-96818, Iran

³ Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717, USA

10.22060/ajmc.2025.24428.1420

Abstract

This article investigates the time-space fractional advection-dispersion equation $(TSFADE)$. In this work, a efficient and precise numerical method (Novel Shifted Jacobi Operational Matrix technique) is applied for solving a category of these equations, converting the original problem into a set of algebraic equations that can be solved using numerical methods. The key benefit of this scheme is its ability to transform linear and nonlinear $(PDEs)$ into a set of algebraic equations concerning the expansion coefficients of the solution. The suggested scheme is effectively utilized for the mentioned problem. Sufficient and thorough numerical evaluations are provided to illustrate the precision, applicability, effectiveness, and adaptability of the introduced scheme. To showcase the efficacy and accuracy of this technique, the numerical results from the examples are presented in a table format to enable comparison with results from other established methods as well as with the precise solutions. It should be noted that the performance of the current method is regarded as quite simple and general for many numerical techniques.

Keywords

Operational matrix

Time-space fractional diffusion equation

Caputo differential operator

Shifted Jacobi polynomials

Subjects