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

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.