QUADRATIC APPROXIMATION OF SOLUTIONS FOR SET-VALUED FUNCTIONAL DIFFERENTIAL EQUATIONS

Peiguang Wang; Yameng Wang

doi:10.11948/20200133

2021 Volume 11 Issue 1

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Peiguang Wang, Yameng Wang. QUADRATIC APPROXIMATION OF SOLUTIONS FOR SET-VALUED FUNCTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 532-545. doi: 10.11948/20200133

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Peiguang Wang, Yameng Wang. QUADRATIC APPROXIMATION OF SOLUTIONS FOR SET-VALUED FUNCTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 532-545. doi: 10.11948/20200133

QUADRATIC APPROXIMATION OF SOLUTIONS FOR SET-VALUED FUNCTIONAL DIFFERENTIAL EQUATIONS

Peiguang Wang^1, ,,
Yameng Wang¹

1.
School of Mathematics and Information Science, Hebei University, The May 4th Street, 071000, China

Corresponding author: Email address: pgwang@hbu.edu.cn(P. Wang)
Fund Project: The authors were supported by National Natural Science Foundation of China (11771115, 11271106)

Abstract

Abstract

This paper investigates nonlinear set-valued functional differential equations with initial value conditions. By introducing the notion of Hukuhara partial derivative of set-valued function, using the comparison principle and the method of quasilinearization, we obtain monotone iterative sequences of approximate solutions which converge uniformly and quadratically to the solutions of such problems.
- Set-valued functional differential equations /
- coupled lower and upper solutions /
- quasilinearization /
- convergence
MSC: 34A12, 34K07, 39B12

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