求解非线性时间分数阶Klein-Gordon方程的谱配置方法  

Spectral Collocation Method for Solving Nonlinear Time-Fractional Klein-Gordon Equation

作　　者：周琴[1] 杨银[2] 

机构地区：[1]湖南涉外经济学院信息科学与工程学院,长沙410205 [2]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《吉林大学学报（理学版）》2018年第2期286-292,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11671342);湖南省自然科学基金(批准号:2016JJ3114);湖南省教育厅重点项目(批准号:17A210);湖南涉外经济学院科学研究一般项目(批准号:2017B10)

摘　　要：用Jacobi谱配置方法,数值求解一类非线性时间分数阶导数为Caputo导数的KleinGordon方程.先用Caputo分数阶导数和Riemann-Liouville分数阶积分的关系,将分数阶Klein-Gordon方程转化为在时间上带奇异核的积分微分方程,再在时间和空间上采用Jacobi谱配置法,并用高斯积分公式逼近积分项,使方程在配置点上成立,从而求得其数值解.数值算例结果表明,该方法所得数值解很好地逼近了精确解.We numerically solved a class of the Klein-Gordon equations with a nonlinear time-fractional derivative of Caputo by using Jacobi spectral collocation method.First,the fractional Klein-Gordon equation was transformed into an integral differential equation with a singular kernel in the time by using the relation between the Caputo fractional derivative and the Riemann-Liouville fractional integral,and then we used a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation.The results show that the numerical solution obtained by this method is a good approximation of the exact solution.

关 键 词：CAPUTO分数阶导数 时间分数阶Klein-Gordon方程 谱配置方法 

分 类 号：O241.82[理学—计算数学]