Selçuk Journal of Applied Mathematics

 Selçuk Journal of
  Applied Mathematics

  Summer-Autumn, 2000
  Volume  1
  Number 1

Research Center of 
  Applied Mathematics

 SJAM Summer-Autumn 2000, Volume 1 - Number 1

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

Vladimir Vaskevich1* ,  Haydar Bulgak2, Cengiz Çinar2  

1 Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia

 2 Research Centre of Applied Mathematics, Selçuk University, Konya, Turkey

Received: August 31, 2000

To Prof. Dr. Chr. Zenger 60-th birthday

Consider an initial value problem for  simultaneous linear difference equations x(n+1) = Ax(n) + f(n), x(0) = a,    with  the   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.


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 NATO-PC Advanced Fellowships Programme.

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