Adams–Simpson method for solving uncertain differential equation

Xiao Wang, Yufu Ning, Tauqir A. Moughal and Xiumei Chen

Applied Mathematics and Computation, 2015, vol. 271, issue C, 209-219

Abstract: Uncertain differential equation is a type of differential equation driven by canonical Liu process. How to obtain the analytic solution of uncertain differential equation has always been a thorny problem. In order to solve uncertain differential equation, early researchers have proposed two numerical algorithms based on Euler method and Runge–Kutta method. This paper will design another numerical algorithm for solving uncertain differential equations via Adams–Simpson method. Meanwhile, some numerical experiments are given to illustrate the efficiency of the proposed numerical algorithm. Furthermore, this paper gives how to calculate the expected value, the inverse uncertainty distributions of the extreme value and the integral of the solution of uncertain differential equation with the aid of Adams–Simpson method.

Keywords: Uncertain differential equation; Numerical solution; Adams–Simpson method (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:271:y:2015:i:c:p:209-219

DOI: 10.1016/j.amc.2015.09.009

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