分数演算的G-L数值算法中加权系数求解  

Solving the weight coefficient of G-L numerical algorithm in the fractional calculus

作　　者：张恒[1] 袁晓[1] 帅晓飞[1] 汤韩杰[1] 陈理[1] 

机构地区：[1]四川大学电子信息学院,成都610064

出　　处：《四川大学学报（自然科学版）》2007年第4期831-834,共4页Journal of Sichuan University(Natural Science Edition)

摘　　要：从分数演算基本的G-L定义出发,引出G-L数值算法中加权系数——G-L加权系数与广义二项式系数之间的关系,进而通过Γ函数来求解G-L加权系数.而后用加权系数的参数构建一个二维平面,使这些参数由整数域拓展到整个实数域,实现了分数演算中加权系数和对应二项式系数的推广.最后利用Matlab语言编程实现,为分数演算的数值计算提供方便、快捷的工具.Start with the Grunwald-Letnikov definition （G-L definition） of the fractional calculus, the relationship between the weight coefficients of the G-L numerical algorithm and the generalized binomial coefficents is introduced. And then , the G-L weight coefficent is obtained by using the gamma function in Matlab. A two-dimensional plane of the G-L weight coefficient and a two-dimensional plane of the generalized binomial coefficient are presented in this paper. Finally , a method how to compute the weight coefficent is given in MATLAB, which is convenient to numerical approximate the fractioanl calculus.

关 键 词：分数微积分 G-L定义 Γ函数 广义二项式系数 MATLAB 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]