含Caputo-Fabrizio分数阶算子的非线性刚性泛函微分方程Runge-Kutta方法的稳定性  

Stability of Runge-Kutta methods for nonlinear stiff functional differential equations with Caputo-Fabrizio fractional operator

作　　者：文立平[1] 杨经纬 WEN Liping;YANG Jingwei(School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105

出　　处：《湘潭大学学报（自然科学版）》2023年第4期8-17,共10页Journal of Xiangtan University(Natural Science Edition)

基　　金：国家自然科学基金(12271463)。

摘　　要：该文针对一类带有Caputo-Fabrizio分数阶算子的非线性刚性泛函微分方程初值问题,利用线性插值技巧离散Caputo-Fabrizio算子,结合求解常微分方程的数值方法,构造了求解该问题的Runge-Kutta方法,给出了在一定条件下方法的非线性稳定性结果.In order to solve the initial value problem for a class of nonlinear stiff functional differential equations with Caputo-Fabrizio fractional operators,the Runge-Kutta methods are constructed by discretized the Caputo-Fabrizio fractional operator using linear interpolation techniques and combined with numerical methods for solving ordinary differential equations.The nonlinear stability results of the methods are given under certain conditions.

关 键 词：非线性刚性泛函微分方程 Caputo-Fabrizio分数阶算子 RUNGE-KUTTA方法 稳定性 代数稳定性 

分 类 号：O241.8[理学—计算数学]