A computational study of variable coefficients fractional advection–diffusion–reaction equations via implicit meshless spectral algorithm

Abstract

In this article, a meshless spectral radial point interpolation method is proposed for the numerical solutions of a class of time-fractional advection–diffusion–reaction equations. The current approach utilizes meshless shape functions, having Kronecker delta function property, for approximation of spatial operators. Forward difference along with quadrature formula is used for tempered fractional derivative approximation in the framework of implicit time marching scheme. Assessment of the proposed method is made by applying to various concrete test problems having constant and variable coefficients. Approximation and function reproduction quality are measured via $${E}_{\\infty }$$E∞, $${E}_{2}$$E2 and $${E}_{\\text {rms}}$$Erms error norms. Comparison of simulated results is also made with available exact solutions as well as earlier reported works. Stability analysis of the proposed method is thoroughly discussed and computationally affirmed.