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Selçuk Journal
of
Applied Mathematics
Summer-Autumn, 2000
Volume 1
Number 1
Research Center
of
Applied Mathematics
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SJAM
Summer-Autumn 2000, Volume 1 - Number 1
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Algorithm with guaranteed accuracy for computing a solution to
an initial value problem for linear difference equations
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Vladimir Vaskevich1* , Haydar Bulgak2, Cengiz
Çinar2 |
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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 60-th birthday
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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 N-dimensional
rational vectors, and a a rational N-dimensional
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. |
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Key
words
initial value problems, simultaneous linear difference equations,
algorithms with guaranteed accuracy, discrete asymptotically stable matrices
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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
NATO-PC Advanced Fellowships Programme.
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Article
in PS format (103 kb) |
Article in ZIP
format (41 kb) |
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