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Doostdar, Mohammad Reza, Kazemi, Manochehr, Vahidi, Alireza. (1402). A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions. سامانه مدیریت نشریات علمی, 11(2), 241-253. doi: 10.22034/cmde.2022.50054.2082
Mohammad Reza Doostdar; Manochehr Kazemi; Alireza Vahidi. "A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions". سامانه مدیریت نشریات علمی, 11, 2, 1402, 241-253. doi: 10.22034/cmde.2022.50054.2082
Doostdar, Mohammad Reza, Kazemi, Manochehr, Vahidi, Alireza. (1402). 'A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions', سامانه مدیریت نشریات علمی, 11(2), pp. 241-253. doi: 10.22034/cmde.2022.50054.2082
Doostdar, Mohammad Reza, Kazemi, Manochehr, Vahidi, Alireza. A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions. سامانه مدیریت نشریات علمی, 1402; 11(2): 241-253. doi: 10.22034/cmde.2022.50054.2082

A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions

Computational Methods for Differential Equations
مقاله 3، دوره 11، شماره 2، تیر 2023، صفحه 241-253    اصل مقاله (374.72 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50054.2082
نویسندگان
Mohammad Reza Doostdar* 1؛ Manochehr Kazemi2؛ Alireza Vahidi3
1Department of Mathematics, Zarandieh Branch, Islamic Azad University, Zarandieh, Iran
2Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran
3Department of Mathematics, Yadegar -e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran
چکیده
This paper presents an efficient numerical method to solve two versions of the Duffing equation by the hybrid functions based on the combination of Block-pulse functions and Legendre polynomials. This method reduces the solution of the considered problem to the solution of a system of algebraic equations. Moreover, the convergence of the method is studied. Some examples are given to demonstrate the applicability and effectiveness of the proposed method. Also, the obtained results are compared with some other results. 
کلیدواژه‌ها
Integral boundary conditions؛ Boundary value problem؛ Duffing equation؛ Hybrid functions؛ Legendre polynomials
مراجع
  • [1] B. Ahmad and B. S. Alghamdi, Approximation of solutions of the non-linear Duffing equation involving both integral and non-integral forcing terms with separated boundary conditions, Comput. Phys. Comm., 179 (2008), 409–416.
  • [2] B. Ahmad and A. Alsaedi, Existence of approximate solutions of the forced Duffing equation with discontinuous type integral boundary conditions, Anal. Real World Appl., 10 (2009), 358–367.
  • [3] B. Ahmad, A. Alsaedi, and B. Alghamdi, Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions, Anal. Real World Appl., 9 (2008), 1727–1740.
  • [4] B. Ahmad, S. K. Ntouyas, and A. Alsaedi, On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions, Chaos Solitons and Fractals, 83 (2016), 234–241.
  • [5] A. M. Alenezi, Hybrid Orthonormal Bernstein and Block-Pulse Method for the Solution of New System of Volterra Integro-differential Equations, Journal of Mathematics Research, 12(5) (2020), 1–20.
  • [6] M. Alshammari, M. Al-Smadi, O. A. Arqub, I. Hashim, and M. A. Alias, Residual Series representation algorithm for solving fuzzy duffing oscillator equations, Symmetry, 12(4) (2020), 572.
  • [7] R. A. Attia, D. Lu, and M. MA Khater, Chaos and relativistic energy-momentum of the nonlinear time fractional Duffing equation, Mathematical and Computational Applications, 24(1) (2019), 10.
  • [8] Z. Azimzadeh, A. R. Vahidi, and E. Babolian, Exact solutions for non-linear Duffing’s equations by He’s homotopy perturbation method, Indian J. Phys., 86 (2012), 721–726.
  • [9] S. Balaji, A new approach for solving Duffing equations involving both integral and non-integral forcing terms, Ain Shams Engineering Journal, 5(3) (2014), 985–990.
  • [10] S. L. Bichi and S. U. Faruk, Numerical Solution of System of Linear Volterra Integral Equations via Hybrid of Taylor and Block-pulse Functions, Bayero Journal of Pure and Applied Sciences, 12(1) (2019), 462–469.
  • [11] B. Bilgehan and A. O¨ zyapıcı, Direct solution of nonlinear differential equations derived from real circuit applica- tions, Analog Integrated Circuits and Signal Processing, 101(3) (2019), 441–448.
  • [12] A. Boucherif, Second order boundary value problems with integral boundary condition, Nonlinear Anal. Theor., 70 (2009), 364–371.
  • [13] C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral methods in fluid dynamics, Springer Verlag, Berlin Heidelberg, 1988.
  • [14] M. Chai and L. Ba, Application of EEG Signal Recognition Method Based on Duffing Equation in Psychological Stress Analysis, Advances in Mathematical Physics, 2021 (2021).
  • [15] Z. Cheng and Q. Yuan, Damped superlinear Duffing equation with strong singularity of repulsive type, Journal of Fixed Point Theory and Applications, 22(2) (2020), 1–18.
  • [16] A. A. Cherevko, E. E. Bord, A. K. Khe, V. A. Panarin, and K. J. Orlov, The analysis of solutions behaviour of Van der Pol Duffing equation describing local brain hemodynamics, Journal of Physics: Conference Series, 894 (1) (2017), 012012.
  • [17] M. R. Doostdar, A. R. Vahidi, T. Damercheli, and E. Babolian, A hybrid functions method for solving linear and non-linear systems of ordinary differential equations, Math. Commun., 26 (2021), 197–213.
  • [18] J. Du and M. Cui, Solving the forced Duffing equation with integral boundary conditions in the reproducing kernel space, Int. J. Comput. Math., 87 (2010), 2088–2100.
  • [19] F. Geng, Numerical solutions of Duffing equations involving both integral and non-integral forcing terms, Comput. Math. Appl., 61 (2011), 1935–1938.
  • [20] F. Geng and M. Cui, New method based on the HPM and RKHSM for solving forced Duffing equations with integral boundary conditions, J. Comput. Appl. Math., 233 (2009), 165–172.
  • [21] J. H. He, A short review on analytical methods for a fully fourth-order nonlinear integral boundary value problem with fractal derivatives, International Journal of Numerical Methods for Heat and Fluid Flow, 30 (2020), 4933– 4943.
  • [22] E. Hesameddini and M. Riahi, Hybrid Legendre Block-Pulse functions method for solving partial differential equations with non-local integral boundary conditions, Journal of Information and Optimization Sciences, 40(7) (2019), 1–13.
  • [23] R. Jafari, R. Ezzati, and K. Maleknejad, A new operational matrix of derivative for hybrid third kind Chebyshev polynomials and Block-pulse functions and its applications in solving second-order differential equations, Tbilisi Mathematical Journal, 14 (2021), 163–179.
  • [24] T. Jankowski, Positive solutions for second order impulsive differential equations involving Stieltjes integral con- ditions, Nonlinear Anal., 74(11) (2011), 3775–3785 .
  • [25] D. Jiang, J. J. Nieto, and W. Zuo, On monotone method for first order and second periodic boundary value problems and periodic solutions of functional differential equation, J. Math. Anal. Appl., 289 (2004), 691–699.
  • [26] E . Kreyszig, Introductory functional analysis with applications, Wiley, New York, 1989.
  • [27] C. W. Lim and B. S. Wu, A new analytical approach to the Duffing-harmonic oscillator, Phys. Lett. A, 311(4–5) (2003), 365–373.
  • [28] L. Liu, B. Liu, and Y. Wu, Nontrivial solutions of m-point boundary value problems for singular second-order differential equations with a sign-changing nonlinear term, J. Comput. Appl. Math., 224(1) (2009), 373–382 .
  • [29] R. Ma and H. Wang, Positive solutions of nonlinear three-point boundary-value problems, Electron. J. Differ. Equ., 279(1) (2003), 216–227.
  • [30] N. Mollahasani, M. M. Moghadam, and G. Chuev, Hybrid Functions of Lagrange Polynomials and Block-Pulse Functions for Solving Integro-partial Differential Equations, Iran. J. Sci. Technol. Trans. Sci., (2018), 1–9.
  • [31] R. Najafi and B. Nemati Saray, Numerical solution of the forced Duffing equations using Legendre multiwavelets, Comput. Methods Differ. Equ., 5 (2017), 43–55.
  • [32] J. J. Nieto and R. Rodriguez-Lopez, Monotone method for first-order functional differential equations, Comput. Appl. Math., 52 (2006), 471–480.
  • [33] R. B. Potts, Best difference equation approximation to Duffing’s equation, J. Aust. Math. Soc. Ser. B, 23(4) (1981/82), 349–356.
  • [34] A. Saadatmandi and F. Mashhadi-Fini, A pseudospectral method for nonlinear Duffing equation involving both integral and non-integral forcing terms, Mathematical Methods in the Applied Sciences, 38(7) (2015), 1265–1272.
  • [35] A. Saadatmandi and S. Yeganeh, New approach for the duffing equation involving both integral and non-integral forcing terms, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 79 (2017), 43–52.
  • [36] A. H. Salas, S. A. El-Tantawy, and N. H. Aljahdaly, An exact solution to the quadratic damping strong nonlinearity Duffing oscillator, Mathematical Problems in Engineering, (2021), Article ID 88755892021.
  • [37] L. J. Sheu, H. K. Chen, J. H. Chen, and L. M. Tam, Chaotic Dynamics of the Fractionally Damped Duffing Equation, Chaos Solitons and Fractals, 32 (2007), 1459–1468.
  • [38] J. J. Stokes, Nonlinear Vibrations, Intersciences, New York, 1950.
  • [39] M. Sun and Y. Xing, Existence results for a kind of fourth-order impulsive integral boundary value problems, Boundary Value Problems, 2016(1) (2016), 1–15.
  • [40] C. Tun¸c and O. Tun¸c, New qualitative criteria for solutions of Volterra integro-differential equations, Arab Journal of Basic and Applied Sciences, 25(3) (2018), 158–165.
  • [41] C. Tun¸c and O. Tun¸c, On the stability, integrability and boundedness analyses of systems of integro-differential equations with time-delay retardation, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 115(3) (2021), 1–17.
  • [42] C. Tun¸c and O. Tun¸c, New results on the qualitative analysis of integro-differential equations with constant time- delay, J. Nonlinear Convex Anal., 23(3) (2022), 435–448.
  • [43] A. R. Vahidi, E. Babolian, and Z. Azimzadeh, An improvement to the homotopy perturbation method for solving nonlinear Duffing’s equations, Bull. Malaysian Math. Sci. Soc., 41 (2017), 1105–1117.
  • [44] A. S. Vatsala and J. Yang, Monotone iterative technique for semi linear elliptic systems, Boundary Value Problems, 2 (2005), 93–106.
  • [45] H. M. Yao, Solution of the Duffing equation involving both integral and non-integral forcing terms, Comput. Phys. Commun., 180 (2009), 1481–1488.
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