[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.
)