A superlinear numerical scheme for multi-term fractional nonlinear ordinary differential equations  

作　　者：Jingna Zhang Haobo Gong Sadia Arshad Jianfei Huang 

机构地区：[1]College of Mathematical Sciences,Yangzhou University Yangzhou 225002,China [2]COMSATS University Islamabad,Lahore Campus,Pakistan

出　　处：《International Journal of Modeling, Simulation, and Scientific Computing》2020年第2期100-114,共15页建模、仿真和科学计算国际期刊（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11701502 and 11871065).

摘　　要：In this paper,we present a superlinear numerical method for multi-term fractional nonlinear ordinary differential equations(MTFNODEs).First,the presented problem is equivalently transformed into its integral form with multi-term Riemann-Liouville integrals.Second,the compound product trapezoidal rule is used to approximate the fractional integrals.Then,the unconditional stability and convergence with the order 1+αN−1−αN−2 of the proposed scheme are strictly established,whereαN−1 andαN−2 are the maximum and the second maximum fractional indexes in the considered MTFNODEs,respectively.Finally,two numerical examples are provided to support the theoretical results.

关 键 词：Multi-term fractional ordinary differential equations nonlinear system numerical method stability convergence 

分 类 号：O17[理学—数学]