Explicit solution of second-order delayed discrete equations
Nazim I. Mahmudov
TL;DR
This paper derives a closed-form solution for a class of second-order delayed discrete equations with noncommutative matrix coefficients, utilizing Z-transform and novel delayed matrix sine/cosine functions.
Contribution
It introduces a new method to explicitly solve second-order delayed difference equations with noncommutative matrix coefficients.
Findings
Closed-form solutions for second-order delayed difference equations derived.
New delayed matrix sine and cosine functions defined and utilized.
Method applicable to systems with noncommutative matrix coefficients.
Abstract
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the Z-transform and determining function.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Mathematical and Theoretical Epidemiology and Ecology Models · Matrix Theory and Algorithms