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This is a Quantitative Study study.

September 26, 2025

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

Key Points

The proposed method enhances accuracy and computational efficiency in solving fractional advection-diffusion equations, validating its superiority.
Utilization of local radial basis functions and a differential quadrature method significantly improves results against the finite volume method.
Three nonhomogeneous test problems were analyzed to assess the efficacy of the new simulation technique, focused on error norms.
The effectiveness of the technique is categorized by examining error norms, fractional orders, convergence rates, and execution times.

Abstract

This articlepresents 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 𝐿∞, 𝐿2error 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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