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

Abstract

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 ≥ 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.

The Stability of Set-Valued Differential Equations with Different Initial Time in the Sense of Fractional-like Hukuhara Derivatives

“…Set-valued differential equations has attracted extensive attention of scholars because of its important applications in system identification, signal processing, optics, thermal, rheology and many other fields. There are some interesting results such as set-valued differential equations [1][2][3][4][5][6][7][8], set-valued functional differential equations [9][10][11][12][13] as well as stochastic set-valued differential equations [14][15][16]. The literature [17,18] systematically summarized the research results of this kind of problems.…”