一类分数阶常微分方程的显式算法  

Explicit Scheme for a Class of Fractional Ordinary Differential Equations

作　　者：陈全发[1] 冯光[2] 肖爱国[2] 

机构地区：[1]湘南学院数学系,郴州423000 [2]湘潭大学数学与计算科学学院,湘潭411105

出　　处：《系统仿真学报》2009年第4期1029-1032,1054,共5页Journal of System Simulation

基　　金：国家自然科学基金(10571147)资助项目;湖南省教育厅科研资助项目(08C825);湖南省科技计划资助项目

摘　　要：利用Caputo导数的性质和求解普通积分方程的Admas技巧,得到一种求解一类分数阶微分方程初值问题的显式方法;证明了其整体误差估计为O(hθ),θ=min{α,2},并进行了稳定性分析。该方法在α>1时比已有的几种显式方法具有更高的数值精度和收敛阶。According to properties of the Caputo derivative and the Admas technique for ordinary integral equations, an explicit numerical scheme for the initial value problems of a class of fractional differential equations was obtained; and its global error was estimated to be O（h^θ）,θ = min{a,2}, and the stability properties were considered. The method can provide higher precision and convergence order than the existing explicit numerical schemes when a 〉 1.

关 键 词：数值分析 分数阶微分方程 CAPUTO导数 显式方法 误差分析 稳定性 

分 类 号：O241.81[理学—计算数学] TP301.6[理学—数学]