A Computational Simulation of Fractional Advection-Diffusion Model Using Differential Quadrature and Local Radial Basis Functions

Arshed ALi; Raza Ali Khan; Imtiaz Ahmad

Authors

Arshed ALi Department of Mathematics, Islamia College Peshawar
Raza Ali Khan Department of Mathematics, Islamia College Peshawar, Pakistan
Imtiaz Ahmad Institue of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional (UNITEN), Kajang, Selangor, Malaysia

Keywords:

Caputo fractional derivative, Differential quadrature, Backward difference formula, Fractional Advection-Diffusion equation, Radial basis functions

Abstract

This article presents a local radial basis function-based differential quadrature method for solving the time-fractional advection-diffusion equation. Backward difference formula is utilized to approximate Caputo fractional derivative. Differential quadrature approach is employed to compute the space derivatives by 3-point central scheme in the neighborhood of a node. Two types of radial basis functions are utilized in numerical simulations. Accuracy and computational efficiency of proposed technique is assessed via , error norms, fractional order, time and spatial step sizes, rate of convergence and execution time. Three nonhomogeneous test problems are solved to validate the method, and the results are compared with finite volume method to show its superiority.

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