A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation

作     者：Yin Yang Jianyong Tao Shangyou Zhang Petr V.Sivtsev 

作者机构：Hunan Key Laboratory for Computation and Simulation in Science and EngineeringKey Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China Department of Mathematical SciencesUniversity of DelawareNewarkDE 19716USA International Scientific and Research Laboratory of Multiscale Model Reduction and High Performance ComputingAmmosov North Eastern UniversityKulakovskogo677013YakutskRussia 

出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)

年 卷 期：2020年第12卷第1期

页      面：57-86页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China Project(Nos.11671342,11771369,11931003) Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(Nos.2018JJ2374,2018WK4006,2019YZ3003) Key Project of Hunan Provincial Department of Education(No.17A210)and mega-grant of the Russian Federation Government(N 14.Y26.31.0013) 

主　　题：The fractional Ginzburg-Landau equation Jacobi collocation method convergence 

摘      要：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 ***,we space-discretize the equation by the Jacobi-Gauss-Lobatto collocation(JGLC)method in one-and two-dimensional *** equation is then converted to a system of ordinary differential equations(ODEs)with the time variable based on *** second step applies the Jacobi-Gauss-Radau collocation(JGRC)method for the time ***,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.