Moment Estimation for Uncertain Delay Differential Equations via the Composite Heun Scheme

Shaoling Zhou (), Huimin Zhang, Chiteng Liu and Xiaosheng Wang ()
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Shaoling Zhou: School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China
Huimin Zhang: School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China
Chiteng Liu: School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China
Xiaosheng Wang: School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China

Mathematics, 2025, vol. 13, issue 21, 1-17

Abstract: As an important mathematical model actuated by the Liu process, uncertain delay differential equations depict the development of system dynamics. In the applications of uncertain delay differential equations, parameter estimation plays a key role. In the paper, a new scheme called the composite Heun scheme is introduced. This scheme is then incorporated into the method of moments to estimate the unknown parameters in uncertain delay differential equations. Some numerical examples are given to illustrate the feasibility of the composite Heun scheme. Two distinct types of uncertain delay differential equations with integer delay time and noninteger delay time are discussed. Finally, we present an uncertain delay stock model to forecast the stock prices of Xiamen Airlines by using the parameter estimation approach proposed in this work.

Keywords: uncertain delay differential equation; composite Heun scheme; method of moments; uncertain delay stock model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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