In this paper linear difference equations with several independent variables are considered, whose solutions are functions defined on sets of $n$-dimensional vectors with integer coordinates. These equations could be called partial difference equations. Existence and uniqueness theorems for these equations are formulated and proved, and interconnections of such results with the theory of linear multidimensional digital systems are investigated.
Numerous examples show essential differences of the results from those of the theory of (one-dimensional) difference equations. The significance and the correct formulation of initial conditions for the solution o partial difference equation is established and methods are described, which make it possible to construct the solution algorithmically. Extensions of the theory to some special nonlinear partial difference equations are also considered.
In this paper linear difference equations with several independent variables are considered, whose solutions are functions defined on sets of $n$-dimensional vectors with integer coordinates. These equations could be called partial difference equations. Existence and uniqueness theorems for these equations are formulated and proved, and interconnections of such results with the theory of linear multidimensional digital systems are investigated.
Numerous examples show essential differences of the results from those of the theory of (one-dimensional) difference equations. The significance and the correct formulation of initial conditions for the solution o partial difference equation is established and methods are described, which make it possible to construct the solution algorithmically. Extensions of the theory to some special nonlinear partial difference equations are also considered.
@article{10_21136_AM_1987_104253,
author = {Bos\'ak, Miroslav and Gregor, Ji\v{r}{\'\i}},
title = {On generalized difference equations},
journal = {Applications of Mathematics},
pages = {224--239},
year = {1987},
volume = {32},
number = {3},
doi = {10.21136/AM.1987.104253},
mrnumber = {0895880},
zbl = {0632.39005},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104253/}
}
TY - JOUR
AU - Bosák, Miroslav
AU - Gregor, Jiří
TI - On generalized difference equations
JO - Applications of Mathematics
PY - 1987
SP - 224
EP - 239
VL - 32
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104253/
DO - 10.21136/AM.1987.104253
LA - en
ID - 10_21136_AM_1987_104253
ER -
%0 Journal Article
%A Bosák, Miroslav
%A Gregor, Jiří
%T On generalized difference equations
%J Applications of Mathematics
%D 1987
%P 224-239
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104253/
%R 10.21136/AM.1987.104253
%G en
%F 10_21136_AM_1987_104253
Bosák, Miroslav; Gregor, Jiří. On generalized difference equations. Applications of Mathematics, Tome 32 (1987) no. 3, pp. 224-239. doi: 10.21136/AM.1987.104253
