Operational matrix approach for solving the variable-order nonlinear Galilei invariant advection–diffusion equation

Abstract

Abstract In this paper, we investigate numerical solution of the variable-order fractional Galilei advection–diffusion equation with a nonlinear source term. The suggested method is based on the shifted Legendre collocation procedure and a matrix form representation of variable-order Caputo fractional derivative. The main advantage of the proposed method is investigating a global approximation for the spatial and temporal discretizations. This method reduces the problem to a system of algebraic equations, which is easier to solve. The validity and effectiveness of the method are illustrated by an easy-to-follow example.

Keywords

• Variable-order derivative
• Nonlinear Galilei invariant advection–diffusion equation
• Collocation method
• Legendre polynomials