一类分数阶非线性微分方程组的显式算法  

Solving a System of Nonlinear Fractional Ordinary Differential Equations by a Explicit Scheme

作　　者：童启秀[1] 王胜兵[1] 

机构地区：[1]海军工程大学理学院,湖北武汉430033

出　　处：《武汉理工大学学报（交通科学与工程版）》2013年第5期1119-1123,共5页Journal of Wuhan University of Technology（Transportation Science & Engineering）

摘　　要：讨论了一类分数阶微分方程组的一种数值算法,根据Caputo导数的性质,将分数阶微分方程组转化为Volterra积分方程组,再利用求解普通积分方程的Adams技巧,建立了分数阶微分方程组的一种显式数值算法,证明了该算法的收敛性与稳定性,并给出了数值仿真实例,证实了算法的有效性.an explicit numerical method for the initial value problems of a system of nonlinear fractional ordinary differential equations was obtained by properties of the Caputo derivative and the Admas technique for ordinary integral equations.Then we have proved the convergence and stability of the method.At last a numerical example is provided which confirm that the method is effective in solving a system of the nonlinear fractional ordinary differential equations.

关 键 词：分数阶显式算法 非线性分数阶微分方程组 收敛性与稳定性 数值仿真 

分 类 号：O175.14[理学—数学]