Publication detail

# Note on some representations of general solutions to homogeneous linear difference equations

STEVIČ, S. IRIČANIN, B. KOSMALA, W. ŠMARDA, Z.

Original Title

Note on some representations of general solutions to homogeneous linear difference equations

English Title

Note on some representations of general solutions to homogeneous linear difference equations

Type

journal article in Web of Science

Language

en

Original Abstract

Here we find all the homogeneous linear difference equations with constant coefficients of any order whose general solution have a representation of a related form. We also present an interesting elementary procedure for finding a representation of general solution to any homogeneous linear difference equation with constant coefficients in terms of the coefficients of the equation, initial values, and an extension of the Fibonacci sequence. This is done for the case when all the roots of the characteristic polynomial associated with the equation are mutually different, and then it is shown that such obtained representation also holds in other cases. It is also shown that during application of the procedure the extension of the Fibonacci sequence appears naturally

English abstract

Here we find all the homogeneous linear difference equations with constant coefficients of any order whose general solution have a representation of a related form. We also present an interesting elementary procedure for finding a representation of general solution to any homogeneous linear difference equation with constant coefficients in terms of the coefficients of the equation, initial values, and an extension of the Fibonacci sequence. This is done for the case when all the roots of the characteristic polynomial associated with the equation are mutually different, and then it is shown that such obtained representation also holds in other cases. It is also shown that during application of the procedure the extension of the Fibonacci sequence appears naturally

Keywords

Homogeneous linear difference equation with constant coefficients; General solution; Representation of solutions; Fibonacci sequence

Released

10.09.2020

ISBN

1687-1847

Periodical

Advances in Difference Equations

Year of study

2020

Number

486

State

US

Pages from

1

Pages to

13

Pages count

13

URL

Documents

BibTex

```
@article{BUT165050,
author="Stevo {Stevič} and Bratislav {Iričanin} and Witold {Kosmala} and Zdeněk {Šmarda}",
title="Note on some representations of general solutions to homogeneous linear difference equations",
annote="Here we find all the homogeneous linear difference
equations with constant coefficients of any order whose general solution have a
representation of a related form. We also present an interesting elementary
procedure for finding a representation of general solution to any homogeneous
linear difference equation with constant coefficients in terms of the coefficients of the
equation, initial values, and an extension of the Fibonacci sequence. This is done for
the case when all the roots of the characteristic polynomial associated with the
equation are mutually different, and then it is shown that such obtained
representation also holds in other cases. It is also shown that during application of the
procedure the extension of the Fibonacci sequence appears naturally",
chapter="165050",
doi="10.1186/s13662-020-02944-y",
howpublished="online",
number="486",
volume="2020",
year="2020",
month="september",
pages="1--13",
type="journal article in Web of Science"
}
```