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"
}