Higher order convergence for a class of set differential equations with initial conditions
Peiguang Wang, Xiran Wu, Huina Liu · Discrete and Continuous Dynamical Systems - S · 2020
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 \begin{document}$ m $\end{document} -hyperconvex/hyperconcave functions ( \begin{document}$ m\ge 1 $\end{document} ), 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.