TY - JOUR
T1 - A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation
AU - Yang , Yin
AU - Tao , Jianyong
AU - Zhang , Shangyou
AU - V. Sivtsev , Petr
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 57
EP - 86
PY - 2019
DA - 2019/12
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0070
UR - https://global-sci.org/intro/article_detail/aamm/13419.html
KW - The fractional Ginzburg-Landau equation, Jacobi collocation method, convergence.
AB - <p style="text-align: justify;">In this paper, we design a collocation method to solve the fractional Ginzburg-Landau equation. A Jacobi collocation method is developed and implemented in two steps. First, we space-discretize the equation by the Jacobi-Gauss-Lobatto collocation (JGLC) method in one- and two-dimensional space. The equation is then converted to a system of ordinary differential equations (ODEs) with the time variable based on JGLC. The second step applies the Jacobi-Gauss-Radau collocation (JGRC) method for the time discretization. Finally, we give a theoretical proof of convergence of this Jacobi collocation method and some numerical results showing the proposed scheme is an effective and high-precision algorithm.</p>