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. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 00051179 |
| DOI: | 10.1134/S0005117924060092 |
