Dynamical behavior analysis of an eighth-order Sharma's method  

作　　者：Xiaofeng Wang Xiaohe Chen Wenshuo Li 

机构地区：[1]School of Mathematical Sciences Bohai University,Jinzhou 121000 Liaoning,P.R.China

出　　处：《International Journal of Biomathematics》2024年第7期217-239,共23页生物数学学报(英文版)

基　　金：supported by the National Natural Science Foundation of China(No.61976027);the Natural Science Foundation of Liaoning Province(No.2022-MS-371);Educational Commission Foundation of Liaoning Province of China(Nos.LJKMZ20221492 and LJKMZ20221498);the Key Project of Bohai University(No.0522xn078).

摘　　要：We analyze the dynamical behavior of an eighth-order Sharma's iterative scheme,which contains a single parameter,with respect to an arbitrary quadratic polynomial using complex analysis.The eighth-order Sharma's iterative scheme is analytically conjugated to a rational operator on the Riemann sphere.We discuss the strange fixed points of the rational operator and present its stable region graph.Additionally,we briefly investigate the superattracting point and the critical point,which have an impact on the Sharma's iterative scheme discussed.Finally,we present the dynamical planes for different parameter values using the complex dynamics tool,which helps us select more effective members of the Sharma's iterative scheme.Numerical experiments are conducted to verify the theoretical results.

关 键 词：Iterative method FRACTAL complex dynamics STABILITY dynamical plane basin of attraction 

分 类 号：O17[理学—数学]