Selçuk Journal
of
Applied Mathematics
SummerAutumn, 2000
Volume 1
Number 1
Research Center
of
Applied Mathematics

SJAM
SummerAutumn 2000, Volume 1  Number 1

Algorithm with guaranteed accuracy for computing a solution to
an initial value problem for linear difference equations

Vladimir Vaskevich^{1*} , Haydar Bulgak^{2}, Cengiz
Çinar^{2} 
^{
1
}
Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
email: vask@math.nsc.ru
^{2}
Research Centre of Applied Mathematics, Selçuk University, Konya,
Turkey
email hbulgak@selcuk.edu.tr
Received: August 31, 2000
To
Prof. Dr. Chr. Zenger 60th birthday

Summary
Consider an initial value problem for simultaneous linear
difference equations
x(n+1)
= Ax(n) + f(n), x(0) = a,
with A the N´N
rational
matrix, {f(n)} a sequence of Ndimensional
rational vectors, and a a rational Ndimensional
vector. The problem has a unique solution; but to compute {x(n)}
in the interval [0,M] with M a nonnegative integer, we
approximate the reals and carry out the elementary arithmetic
operations in special way. By means of this algorithm, we solve the
initial value problem for a discrete asymptotically stable matrix
A with guaranteed accuracy. 

Key
words
initial value problems, simultaneous linear difference equations,
algorithms with guaranteed accuracy, discrete asymptotically stable matrices

Mathematics Subject Classification (1991):
65F30,
65G10
^{
*}
The research was financially supported by the Scientific and
Technical Research Council of Turkey (TUBITAK) in the framework of a
NATOPC Advanced Fellowships Programme.

Article
in PS format (103 kb) 
Article in ZIP
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