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Analysis of Peak Effects in the Solutions of a Class of Difference Equations.

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Title: Analysis of Peak Effects in the Solutions of a Class of Difference Equations.
Authors: Shcherbakov, P. S.1,2 (AUTHOR) cavour118@mail.ru
Source: Automation & Remote Control. Jun2024, Vol. 85 Issue 6, p512-521. 10p.
Subjects: Linear equations, Class differences, Large deviations (Mathematics), Equilibrium
Abstract: We consider a class of well-known high-order trinomial linear difference equations and analyze the non-asymptotic behavior of their solutions under non-zero initial conditions from the unit box. It is shown that, for certain subsets of coefficients in the stability domain, there always exist initial conditions leading to peak, a large deviation of solutions from the equilibrium position, and that these deviations may take arbitrarily large values. Various special cases are studied, numerical examples are presented. [ABSTRACT FROM AUTHOR]
Copyright of Automation & Remote Control is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: We consider a class of well-known high-order trinomial linear difference equations and analyze the non-asymptotic behavior of their solutions under non-zero initial conditions from the unit box. It is shown that, for certain subsets of coefficients in the stability domain, there always exist initial conditions leading to peak, a large deviation of solutions from the equilibrium position, and that these deviations may take arbitrarily large values. Various special cases are studied, numerical examples are presented. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Automation & Remote Control is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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