A Linear Implicit L1-Legendre Galerkin Chebyshev Collocation Method for Generalized Time- and Space-Fractional Burgers Equation (Journal of Computational Mathematics, 2019)
In this paper, a linear implicit L1-Legendre Galerkin Chebyshev collocation method forthe generalized time- and space-fractional Burgers equation is developed. A linear implicitfinite difference scheme based on the L1-algorithm for the Caputo fractional derivative isproposed for temporal discretization. And the Legendre Galerkin Chebyshev collocationmethod, based on the Legendre-Galerkin variational form, but the nonlinear term andthe right-hand term are treated by Chebyshev-Gauss interpolation, is proposed for spatial discretization. Rigorous stability and convergence analysis are developed. Numericalexamples are shown to demonstrate the accuracy, stability and effectiveness of the method.
Keywords: Generalized fractional Burgers equation; Stability and convergence analysis; Legendre Galerkin Chebyshev collocation method; Finite difference method.