Publication detail

# Representation of solutions of higher-order linear discrete systems

DIBLÍK, J. MENCÁKOVÁ, K.

Original Title

Representation of solutions of higher-order linear discrete systems

English Title

Representation of solutions of higher-order linear discrete systems

Type

conference paper

Language

en

Original Abstract

A linear discrete homogenous system of the order $(m+2)$: \Delta^2 x(k) + B^2 x(k-m)= f(k), k \in\bN_0 is considered where B is a constant n \times n regular matrix, m \in \bN_0 and x\colon \{ -m, -m+1, \dots\} \to \bR^n, f\colon\bZ_0^{\infty} \rightarrow \bR^n. Two linearly independent solutions are found as a special matrix functions called delayed discrete cosine and delayed discrete sine. Utilizing these matrix functions formulas for solutions are derived. An example illustrating results is given as well.

English abstract

A linear discrete homogenous system of the order $(m+2)$: \Delta^2 x(k) + B^2 x(k-m)= f(k), k \in\bN_0 is considered where B is a constant n \times n regular matrix, m \in \bN_0 and x\colon \{ -m, -m+1, \dots\} \to \bR^n, f\colon\bZ_0^{\infty} \rightarrow \bR^n. Two linearly independent solutions are found as a special matrix functions called delayed discrete cosine and delayed discrete sine. Utilizing these matrix functions formulas for solutions are derived. An example illustrating results is given as well.

Keywords

delayed cosine; delayed sine; discrete equation

Released

15.06.2017

Publisher

Univerzita obrany

Location

Brno

ISBN

978-80-7231-417-1

Book

Matematika, informační technologie a aplikované vědy

Edition number

1

Pages from

1

Pages to

9

Pages count

9

URL

Documents

BibTex


@inproceedings{BUT137196,
author="Josef {Diblík} and Kristýna {Mencáková}",
title="Representation of solutions of higher-order linear discrete systems",
annote="A linear discrete homogenous system of the order $(m+2)$: \Delta^2 x(k) + B^2 x(k-m)= f(k), k \in\bN_0 is considered where B is a constant n \times n regular matrix, m \in \bN_0 and x\colon \{ -m, -m+1, \dots\} \to \bR^n, f\colon\bZ_0^{\infty} \rightarrow \bR^n. Two linearly independent solutions are found as a special matrix functions called delayed discrete cosine and delayed discrete sine. Utilizing these matrix functions formulas for solutions are derived. An example illustrating results is given as well.",
}