The Crank‐Nicolson/interpolating stabilized element‐free Galerkin method to investigate the fractional Galilei invariant advection‐diffusion equation
Mostafa Abbaszadeh, Mehdi Dehghan
Abstract
Recently, finding a stable and convergent numerical procedure to simulate the fractional partial differential equations (PDEs) is one of the interesting topics. Meanwhile, the fractional advection‐diffusion equation is a challenge model numerically and analytically. This paper develops a new meshless numerical procedure to simulate the fractional Galilei invariant advection‐diffusion equation. The fractional derivative is the Riemann‐Liouville fractional derivative sense. At the first stage, a difference scheme with the second‐order accuracy has been employed to get a semi‐discrete plan. After this procedure, the unconditional stability has been investigated, analytically. At the second stage, a meshless weak form based upon the interpolating stabilized element‐free Galerkin (ISEFG) method has been used to achieve a full‐discrete scheme. As for the full‐discrete scheme, the order of convergence is . Two examples are studied, and simulation results are reported to verify the theoretical results.