@Article{AAMM-12-1,
author = {Yin, Yang and Tao, Jianyong and Zhang, Shangyou and V., Sivtsev, Petr},
title = {A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2020},
volume = {12},
number = {1},
pages = {57--86},
abstract = {<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>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2019-0070},
url = {https://global-sci.com/article/73026/a-jacobi-collocation-method-for-the-fractional-ginzburg-landau-differential-equation}
}