American Institute of Mathematical Sciences

Higher order convergence for a class of set differential equations with initial conditions

 College of Mathematics and Information Science, Hebei University, Baoding, Hebei 071002, China

* Corresponding author: Peiguang Wang

Received  July 2019 Revised  August 2019 Published  April 2020

Fund Project: The first author is supported by the National Natural Science Foundation of China (grant number 11771115, 11271106)

In this paper, we obtain some rapid convergence results for a class of set differential equations with initial conditions. By introducing the partial derivative of set valued function and the $m$-hyperconvex/hyperconcave functions ($m\ge 1$), and using the comparison principle and quasilinearization, we derive two monotone iterative sequences of approximate solutions of such equations that involve the sum of two functions, and these approximate solutions converge uniformly to the unique solution with higher order.

Citation: Peiguang Wang, Xiran Wu, Huina Liu. Higher order convergence for a class of set differential equations with initial conditions. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020342
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