Abstract
A numerical method is developed to solve ill-conditioned quasilinear equations of nonlinear dynamics of lengthy systems (LS). It is based on different types of factorization of the governing equations. As a result of layer-by-layer time decomposition, original singularity disappears and well-conditioned systems of linear equations are solved numerically. An additional positive effect is reduction of oscillations and monotonization of the profile of the numerical solution, stability of calculation of complex transient processes in the LS (acceleration, jerking, spatial evolution, nonlinear oscillations, etc.).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. V. Sergienko, V. K. Zadiraka, and O. M. Lytvyn, Elements of the General Theory of Optimal Algorithms and Related Issues [in Ukrainian], Naukova Dumka, Kyiv (2012).
I. N. Molchanov, Computer Methods to Solve Problems in Applied Mathematics: Algebra, Approximation of Functions, Ordinary Differential Equations [in Russian], Naukova Dumka, Kyiv (2007).
A. V. Gladky, I. V. Sergienko, and V. V. Skopetsky, Numerical and Analytical Methods for the Analysis of Wave Processes [in Russian], Naukova Dumka, Kyiv (2001).
A. V. Gladky, “Analysis of splitting algorithms in convection–diffusion problems,” Cybern. Syst. Analysis, Vol. 50, No. 4, 548–559 (2014).
A. V. Gladky and V. V. Skopetsky, “Numerical modeling and optimization of one-way wave processes in inhomogeneous media,” Cybern. Syst. Analysis, Vol. 46, No. 5, 845–854 (2010).
O. V. Popov, “Parallel algorithms for factorization of sparse matrices,” Komp. Matematika, Issue 2, 115–124 (2013).
A. Yu. Baranov, “Factorization of nonsymmetric band matrices on computers with graphic accelerators,” in: Proc. 6th All-Ukrainian Scientific and Practical Conference with International Participation “Informatics and Systemic Sciences, March 19–21, 2015, PUET, Poltava (2015).
Yu. I. Kalyukh, “Statics, dynamics, and optimization of rope systems in a stream,” Author’s PhD Theses, GPNTB Ukr., No. 05 94 000783 (1994).
O. M. Trofymchuk, Yu. I. Kaliukh, V. A. Dunin, and Y. A. Berchun, “On the possibility of multi-wavelength identification of defects in piles,” Cybern. Syst. Analysis, Vol. 54, No. 4, 600–609 (2018).
P. J. Roache, Computational Fluid Dynamics, Hermosa Publ. (1972).
G. Farenyuk, I. Kaliukh, E. Farenyuk, T. Kaliukh, Y. Berchun, and V. Berchun, “Experimental and theoretical diagnostics of ferroconcrete piles base on reflection of longitudinal and transverse waves,” Intern. fib Symp. “High tech concrete: Where technology and engineering meet!” Maastricht, The Netherlands, 12–14 June (2017), pp. 1307–1317.
R. W. Bettles and D. A. Chapman, “Experimental verification of a towed body and cable dynamic response theory,” Ocean Eng., Vol. 12, No. 5, 453–469 (1985).
A. N. Trofimchuk, A. M. Gomilko, and O. A. Savitsky, Dynamics of Porous Elastic Fluid-Saturated Media [in Russian], Naukova Dumka, Kyiv (2003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2019, pp. 117–128.
Rights and permissions
About this article
Cite this article
Kaliukh, Y.I., Vusatiuk, A.Y. Factorization in Problems of Control and Dynamics of Lengthy Systems. Cybern Syst Anal 55, 274–283 (2019). https://doi.org/10.1007/s10559-019-00132-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-019-00132-9