TY - JOUR
T1 - A Linear Implicit L1-Legendre Galerkin Chebyshev Collocation Method for Generalized Time- and Space-Fractional Burgers Equation
AU - Yang , Yubo
AU - Ma , Heping
JO - Journal of Computational Mathematics
VL - 5
SP - 629
EP - 644
PY - 2019
DA - 2019/03
SN - 37
DO - http://doi.org/10.4208/jcm.1807-m2017-0197
UR - https://global-sci.org/intro/article_detail/jcm/13038.html
KW - Generalized fractional Burgers equation, Stability and convergence analysis, Legendre Galerkin Chebyshev collocation method, Finite difference method.
AB - <p style="text-align: justify;">In this paper, a linear implicit L1-Legendre Galerkin Chebyshev collocation method for
the generalized time- and space-fractional Burgers equation is developed. A linear implicit
finite difference scheme based on the L1-algorithm for the Caputo fractional derivative is
proposed for temporal discretization. And the Legendre Galerkin Chebyshev collocation
method, based on the Legendre-Galerkin variational form, but the nonlinear term and
the right-hand term are treated by Chebyshev-Gauss interpolation, is proposed for spatial discretization. Rigorous stability and convergence analysis are developed. Numerical
examples are shown to demonstrate the accuracy, stability and effectiveness of the method.</p>