Moment estimation based on the composite Heun scheme for parameters in uncertain differential equations

Article type: Research Article

Authors: Zhou, Shaoling | Tan, Xiaoman | Wang, Xiaosheng^{; *}

Affiliations: School of Mathematics and Physics, Hebei University of Engineering, Handan, China

Correspondence: [*] Corresponding author. Xiaosheng Wang, School of Mathematics and Physics, Hebei University of Engineering, Handan, China. E-mail: xswang@hebeu.edu.cn.

Abstract: Uncertain differential equations are widely used in the fields of finance, chemistry, and so forth. In this paper, the problem of parameter estimation in uncertain differential equations is discussed. The trapezoidal scheme is derived to approximate the uncertain differential equations, then a difference scheme named the composite Heun scheme is proposed to obtain the difference equations of uncertain differential equations. The method of moments based on the composite Heun scheme is given to estimate the parameters in uncertain differential equations. Several examples are used to illustrate the viability of the composite Heun scheme.

Keywords: Composite Heun scheme, uncertain differential equation, method of moments, parameter estimation

DOI: 10.3233/JIFS-230288

Journal: Journal of Intelligent & Fuzzy Systems, vol. 45, no. 3, pp. 4239-4248, 2023