Jacobi Collocation Methods for Solving Generalized Space-Fractional Burgers' Equations

摘要

The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gauss-Lobatto collocation points.By means of the simplified Jacobi operational matrix,we produce the differentiation matrix and transfer the space-fractional Burgers' equation into a system of ordinary differential equations that can be solved by the fourth-order Runge-Kutta method.The numerical simulations indicate that the Jacobi spectral collocation method is highly accurate and fast convergent for the generalized space-fractional Burgers' equation.