A novel Hermite RBF-based differential quadrature method for solving two-dimensional variable-order time fractional advection-diffusion equation with Neumann boundary condition

TL;DR

This paper introduces a new Hermite RBF-based differential quadrature method tailored for accurately solving two-dimensional variable-order time fractional advection-diffusion equations with Neumann boundary conditions, demonstrating robustness and versatility.

Contribution

The paper presents a novel Hermite RBF-DQ method that effectively handles derivative boundary conditions and applies it to complex fractional PDEs with irregular geometries.

Findings

Method accurately solves variable-order fractional PDEs.

Numerical results confirm robustness and versatility.

Effective for irregular geometries and boundary conditions.

Abstract

In this paper, a novel Hermite radial basis function-based differential quadrature method (H-RBF-DQ) is presented. This new method is designed to treat derivative boundary conditions accurately. The developed method is very different from the original Hermite RBF method. In order to illustrate the specific process of this method, although the method can be used to study most of partial differential equations, the numerical simulation of two-dimensional variable-order time fractional advection-diffusion equation is chosen as an example. For the general case of irregular geometry, the meshless local form of RBF-DQ was used and the multiquadric type of radial basis functions are selected for the computations. The method is validated by the documented test examples involving variable-order fractional modeling of air pollution. The numerical results demonstrate the robustness and the versatility of the proposed approach.