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Parameter estimation in uncertain differential equations based on the solution
Author(s) -
Sheng Yuhong,
Zhang Nan
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7370
Subject(s) - mathematics , differential equation , euler method , estimation theory , exact differential equation , integrating factor , mathematical analysis , first order partial differential equation , euler's formula , differential algebraic equation , ordinary differential equation , statistics
The parameter estimation of uncertain differential equation is a significant subject in uncertainty theory. This paper introduces three methods for uncertain differential equations to estimate parameters. These three methods are based on different forms of solutions, and they are the solution of the linear uncertain differential equation, the solution of uncertain differential equation with the Euler scheme, and the solution of uncertain differential equation with the midpoint scheme. According to the correlation operation of the solution obeying the same distribution as that of the observed value, the unknown parameters can be obtained. Several numerical examples are used to illustrate the proposed parameter estimation methods.