Affiliation:
1. Ramanujan Institute for Advanced Study in Mathematics, University of MadrasChennai 600 005, Tamil Nadu, India
Abstract
A direct method to construct integrals for an
N
th-order autonomous ordinary difference equation (
O
Δ
E
):
w
n
+
N
=
F
(
w
n
, …,
w
n
+
N
−1
) is presented. As an illustration we first consider third-order autonomous
O
Δ
E w
n
+3
=
F
(
w
n
,
w
n
+1
,
w
n
+2
) and identify the forms of
F
for which two independent integrals exist. The effectiveness of the method to construct two or more integrals for fourth- and fifth-order
O
Δ
E
s is also demonstrated. The question of integrability of each of the identified difference equations with more than one integral is also discussed.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
5 articles.
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