谱-Galerkin方法求解分数阶偏积分微分方程(英文)  

Spectral-Galerkin Methods for Solving Fractional Order Partial Integro-Differential Equations

作　　者：李物兰[1] 白宝钢[1] 李胜军[2] 胡晓晓[1] 韩艳敏[1] 

机构地区：[1]温州医科大学信息与工程学院,中国温州325035 [2]海南大学信息学院,中国海口570228

出　　处：《湖南师范大学自然科学学报》2013年第6期1-6,共6页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金资助项目(10971062);浙江省教育厅科研资助项目(Y201328047);海南省自然科学基金资助项目(113001)

摘　　要：研究了带弱奇异核分数阶偏积分微分方程的初边值问题.首先,在空间方向用谱Galerkin方法得到空间半离散格式,然后证明了该格式的稳定性和误差估计,收敛率体现了"谱精度";在时间方向采用了中心差分,积分项采用了Lagrange内插法进行离散得到时空全离散格式.最后用数值实验检验了该方法的有效性,同时也确保了理论分析的准确性.Spectral-Galerkin methods for the initial-boundary value problem of the fractional order partial integro-differential equations with a weakly singular kernel is considered .First, in space direc-tion, the semi-discrete scheme is derived by using spectral-Galerkin methods , the stability and error esti-mates of the scheme are proved , the convergence rate shows “spectral accuracy”.Then, in time direc-tion by the center differential , the integral term is treated by the Lagrange interpolation , the fully discrete scheme is achieved based on the semi-discrete scheme.Finally, a numerical experiment is presented to demonstrate the effectiveness of the method and confirm the theoretical results .

关 键 词：谱Galerkin方法 分数阶偏积分微分方程 弱奇异核 稳定性 误差估计 

分 类 号：O241.82[理学—计算数学]