تعداد نشریات | 7 |
تعداد شمارهها | 399 |
تعداد مقالات | 5,389 |
تعداد مشاهده مقاله | 5,288,012 |
تعداد دریافت فایل اصل مقاله | 4,882,750 |
An efficient computational approach for numerical solution of non-smooth dynamical systems | ||
AUT Journal of Mathematics and Computing | ||
مقاله 1، دوره 6، شماره 1، فروردین 2025، صفحه 1-8 اصل مقاله (844.72 K) | ||
نوع مقاله: Original Article | ||
شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22596.1180 | ||
نویسندگان | ||
Mohammad Ali Mehrpouya* 1؛ Hossein Heidary2 | ||
1Department of Mathematics, Tafresh University, P.O. Box 39518-79611, Tafresh, Iran | ||
2Department of Mechanical Engineering, Tafresh University, P.O. Box 39518-79611, Tafresh, Iran | ||
چکیده | ||
In this paper, an efficient computational approach based on the fantastic Simpson integral formula is developed for the numerical solution of nonsmooth dynamical equations. In the proposed approach, at first, the integral reformulation of the target problem is intended. Then, the Simpson formula is employed to discretize the obtained integral equation. It is mentioned that, the implementation of the method is simple, so, the method can be simply and quickly used to solve a wide variety of non-smooth dynamical systems arising in the various engineering models. Numerical experiments of two benchmark examples are presented at the end and the efficiency of the method is reported. | ||
کلیدواژهها | ||
Non-smooth dynamical equation؛ Integral equation؛ Simpson formula؛ System of algebraic equations | ||
مراجع | ||
[1] V. Acary and B. Brogliato, Numerical methods for nonsmooth dynamical systems: applications in mechanics and electronics, Lecture Notes in Applied and Computational Mechanics, Springer-Verlag, Berlin, Heidelberg, 2008. [2] K. E. Atkinson, The numerical solution of integral equations of the second kind, vol. 4 of Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, 1997. [3] K. E. Atkinson, W. Han, and D. E. Stewart, Numerical Solution of Ordinary Differential Equations, John Wiley & Sons, Ltd, 2009. [4] E. Auer and S. Kiel, Uses of verified methods for solving non-smooth initial value problems, Reliable Computing, 19 (2013), pp. 156–175. [5] R. L. Burden, J. D. Faires, and A. M. Burden, Numerical Analysis, Cengage Learning, 10th ed., 2016. [6] H. R. Erfanian, M. N. Skandari, and A. Kamyad, A numerical approach for nonsmooth ordinary differential equations, Journal of Vibration and Control, 19 (2013), pp. 2124–2136. [7] A. F. Filippov, Differential equations with discontinuous righthand sides: control systems, vol. 18, Springer Science & Business Media, 2013. [8] M. Ghaznavi and M. N. Skandari, An efficient pseudo-spectral method for nonsmooth dynamical systems, Iranian Journal of Science and Technology, Transactions A: Science, 42 (2018), pp. 635–646. [9] R. Leine, Bifurcations in discontinuous mechanical systems of Filippov’s type, PhD thesis, Technische Universiteit Eindhoven, Eindhoven, Netherlands, 2000. [10] , Non-smooth stability analysis of the parametrically excited impact oscillator, International Journal of Non-Linear Mechanics, 47 (2012), pp. 1020–1032. [11] R. Leine and D. V. Campen, Bifurcation phenomena in non-smooth dynamical systems, European Journal of Mechanics-A/Solids, 25 (2006), pp. 595–616. [12] R. Leine, D. V. Campen, and C. Glocker, Nonlinear dynamics and modeling of various wooden toys with impact and friction, Journal of Vibration and Control, 9 (2003), pp. 25–78. [13] R. I. Leine and H. Nijmeijer, Dynamics and bifurcations of non-smooth mechanical systems, vol. 18, Springer Science & Business Media, 2013. [14] S. Mahmoud and X. Chen, A verified inexact implicit Runge-Kutta method for nonsmooth ODEs, Numer. Algorithms, 47 (2008), pp. 275–290. [15] M. A. Mehrpouya and M. K. e Oshagh, An efficient numerical solution for time switching optimal control problems, Computational Methods for Differential Equations, 9 (2021), pp. 225–243. [16] M. A. Mehrpouya and S. Fallahi, A modified control parametrization method for the numerical solution of bang-bang optimal control problems, Journal of Vibration and Control, 21 (2015), pp. 2407–2415. [17] M. A. Mehrpouya and M. Shahini, The use of the trapezoidal method for solving the tacoma narrows bridge model, International Journal of Nonlinear Analysis and Applications, 14 (2023), pp. 67–72. [18] N. S. Nedialkov and M. V. Mohrenschildt, Rigorous simulation of hybrid dynamic systems with symbolic and interval methods, in Proceedings of the 2002 American Control Conference (IEEE Cat. No. CH37301), vol. 1, IEEE, 2002, pp. 140–147. [19] I. Sgura, A finite difference approach for the numerical solution of non-smooth problems for boundary value odes, Mathematics and Computers in Simulation, 95 (2014), pp. 146–162. [20] Z. T. Zhusubaliyev and E. Mosekilde, Bifurcations and chaos in piecewise-smooth dynamical systems, vol. 44, World Scientific, Singapore, 2003. | ||
آمار تعداد مشاهده مقاله: 410 تعداد دریافت فایل اصل مقاله: 145 |