References
V. V. Ivanov, Computer Computation Methods, A Handbook [in Russian], Naukova Dumka, Kiev (1986).
E. Hayrer, S. Nersett, and G. Wanner, Solution of Ordinary Differential Equations. Non-Stiff Problems [Russian translation], Mir, Moscow (1990).
A. G. Werschulz, “Computational complexity of one-step methods for systems of differential equations,” Math. Comput.,34, No. 149, 155–174 (1980).
Ker-I Ko, “On the computational complexity of ordinary differential equations” Infor. Contr.,58, No. 1-3 157–194 (1983).
I. N. Molchanov, M. F. Yakovlev, and E. G. Geets, “Some methods of integration of ordinary differential equations on multiprocessor computers,” Kibernetika, No. 5, 10–21 (1983).
G. J. Cooper and R. Vignesvaran, “On the use of parallel processors for implicit Runge-Kutta methods,” Computing,51, No. 2, 135–150 (1993).
J. F. Traub and H. Wozniakowski, A General Theory of Optimal Algorithms [Russian translation], Mir, Moscow (1983).
E. Oran and J. Boris, Numerical Simulation of Reactive Flows [Russian translation], Mir, Moscow (1990).
D. Knuth, The Art of Computer Programming [Russian translation], Vol. 2, Mir, Moscow (1977).
N. S. Bakhvalov, Computational Methods for Solving Ordinary Differential Equations [in Russian], Inst. Kibern. AN UkrSSR, Kiev (1970).
P. N. Besarab, “Numerical methods of constructing rigid body attitude parameters,” Zh. Vychisl. Matom. Mat. Fiziki,10, No. 3, 698–708 (1978).
Algorithms, Software, and Architecture for Multiprocessor Computing Systems [in Russian], Nauka, Moscow (1982).
R. W. Hockney and C. R. Jesshope, Parallel Computers: Architecture, Programming, and Algorithms [Russian translation], Radio i Svyaz', Moscow (1986).
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 122–130, May–June, 1996.
Rights and permissions
About this article
Cite this article
Besarab, P.N. Computational complexity of integrating ordinary differential equations. Cybern Syst Anal 32, 417–423 (1996). https://doi.org/10.1007/BF02366506
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02366506