Variational iteration method for solving uncertain differential equations

Article type: Research Article

Authors: Li, Wanping | Zhang, Guidong | Sheng, Yuhong^{; *}

Affiliations: College of Mathematical and System Sciences, Xinjiang University, Urumqi, China

Correspondence: [*] Corresponding author. Yuhong Sheng, College of Mathematical and System Sciences, Xinjiang University, Urumqi 830046, China. Tel.: +86 18167978160; E-mail: [email protected].

Abstract: Solving uncertain differential equations is a critical subject in the field of uncertainty theory, where uncertain differential equations are a sort of differential equations that involve Liu processes. Currently, considerable effort has been put into addressing this issue. Regrettably, analytic solutions to uncertain differential equations are not always accessible. As a result, several numerical methods have been investigated. However, numerical methods have certain limitations in terms of providing a continuous representation of the solution as well as more information about the solution. This paper will propose a novel algorithm based on the variational iteration method (VIM) for solving uncertain differential equations analytically or approximately analytically. The associated numerical experiments show that the proposed method is an efficient tool for solving uncertain differential equations.

Keywords: Uncertain differential equation, analytic solution, variational iteration method, uncertainty theory

DOI: 10.3233/JIFS-223593

Journal: Journal of Intelligent & Fuzzy Systems, vol. 44, no. 4, pp. 6453-6461, 2023