Volume 12, Issue 1
A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation

Yin Yang ,  Jianyong Tao ,  Shangyou Zhang and Petr V. Sivtsev


Adv. Appl. Math. Mech., 12 (2020), pp. 57-86.

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  • Abstract

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.

  • History

Published online: 2019-12

  • AMS Subject Headings

35R35, 65M12, 65M70

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