利用Laplace变换的分布阶微分方程数值解法  

Numerical Solution of Distributed Order Differential Equation Using Laplace Transform

作　　者：王征[1] 胡长流 

机构地区：[1]郑州大学西亚斯国际学院,河南新郑451150 [2]河南大学数学与统计学院,河南开封475004

出　　处：《湘潭大学自然科学学报》2018年第1期15-18,共4页Natural Science Journal of Xiangtan University

基　　金：河南省基础与前沿技术研究计划项目(122300410381)

摘　　要：提出一种基于Laplace变换的求解分布阶微分方程的数值解法.首先,使用一种隐式梯形规则来离散化分布阶FDE积分为一个求和等式,即将分布阶FDE转化为多项式FDE.然后,基于Riemann-Liouville和Caputo分数阶导数的Laplace变换原理,对积分区间离散化后产生的多项式FDE进行求解.实例结果表明,该方法能够求解分布阶FDE,且具有较好的收敛性和准确性.A numerical solution for the distributed order differential equation based on Laplace transform is proposed.Firstly,an implicit trapezoidal rule is used to discretize the distributed order FDE integrals into a finite sum of equations,so as to convert the distributed order FDE into polynomial FDE.Then,based on the Laplace transform principle of Riemann-Liouville and Caputo fractional derivatives,the polynomial FDE generated after the discretization of the integration interval is solved.The experimental results show that this method can solve distributed FDE with good convergence and accuracy.

关 键 词：分数阶微分方程(FDE) 分布阶微分方程 LAPLACE变换 

分 类 号：O241.8[理学—计算数学]