A novel local Hermite radial basis function-based differential quadrature method for solving two-dimensional variable-order time fractional advection-diffusion equation with Neumann boundary conditions

A novel Hermite radial basis function-based differential quadrature (H-RBF-DQ) method is presented in this paper based on 2D variable order time fractional advection-diffusion equations with Neumann boundary conditions. The proposed method is designed to treat accurately for derivative boundary conditions, which considerably improve the approximation results and extend the range of applicability for the method of RBF-DQ. The advantage of the present method is that the Hermite interpolation coefficients are only dependent of the point distribution yielding a substantially better imposition of boundary conditions, even for time evolution. The proposed algorithm is thoroughly validated and is demonstrated to handle the fractional calculus problems with both Dirichlet and Neumann boundaries very well.