Author:
Wang Peiguang,Wu Xiran,Liu Huina
Abstract
<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ m $\end{document}</tex-math></inline-formula>-hyperconvex/hyperconcave functions (<inline-formula><tex-math id="M2">\begin{document}$ m\ge 1 $\end{document}</tex-math></inline-formula>), 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.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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