Accès libre

On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method

À propos de cet article

Citez

Nayfeh A H, Perturbation Method, 1st ed. Wiley, New York, 1973. NayfehA H Perturbation Method 1st ed Wiley New York 1973 Search in Google Scholar

Nayfeh AH, Introduction to Perturbation Techniques, 1st ed. Wiley, New York, 1981. NayfehAH Introduction to Perturbation Techniques 1st ed Wiley New York 1981 Search in Google Scholar

Rahman MH, Haque BI and Akbar MA, Asymptotic Solution of Fourth Order Near Critically Damped Nonlinear Systems, Journal of information and Mathematical Science, 2009; 1: 61–73. RahmanMH HaqueBI AkbarMA Asymptotic Solution of Fourth Order Near Critically Damped Nonlinear Systems Journal of information and Mathematical Science 2009 1 61 73 Search in Google Scholar

Rahman H, Haque BI and Akbar MA, An Analytical Solutions for Fourth Order Damped-Oscillatory Nonlinear Systems, Research Journal of Mathematics and Statistics, 2011; 3:12–19. RahmanH HaqueBI AkbarMA An Analytical Solutions for Fourth Order Damped-Oscillatory Nonlinear Systems Research Journal of Mathematics and Statistics 2011 3 12 19 Search in Google Scholar

Alam A, Rahman H, Haque BI and Akbar MA, Perturbation technique for analytical solutions of fourth order near critically damped nonlinear systems, International Journal of Basic & Applied Sciences, 2011; 11(1): 81–88. AlamA RahmanH HaqueBI AkbarMA Perturbation technique for analytical solutions of fourth order near critically damped nonlinear systems International Journal of Basic & Applied Sciences 2011 11 1 81 88 Search in Google Scholar

Haque BI, Alam A and Rahman H, Perturbation Solutions of Fourth Order Damped Oscillatory Nonlinear Systems, International Journal of Basic & Applied Sciences, 2011; 11(3). HaqueBI AlamA RahmanH Perturbation Solutions of Fourth Order Damped Oscillatory Nonlinear Systems International Journal of Basic & Applied Sciences 2011 11 3 Search in Google Scholar

Mickens RE, Comments on the method of Harmonic Balance, Journal of Sound Vibration, 1984; 94: 456–460. MickensRE Comments on the method of Harmonic Balance Journal of Sound Vibration 1984 94 456 460 10.1016/S0022-460X(84)80025-5 Search in Google Scholar

Mickens RE, Nonlinear Oscillations, 1st ed. Cambridge University Press, New York, 1991. MickensRE Nonlinear Oscillations 1st ed Cambridge University Press New York 1991 Search in Google Scholar

Mickens RE, Ramadhani I, Investigations of an anti-symmetric quadratic nonlinear oscillator, Journal of Sound and Vibration, 1992; 155:190–193. MickensRE RamadhaniI Investigations of an anti-symmetric quadratic nonlinear oscillator Journal of Sound and Vibration 1992 155 190 193 10.1016/0022-460X(92)90657-J Search in Google Scholar

Lim CW and Wu BS, A modified procedure for certain non-linear oscillators, Journal of Sound and Vibration, 2002; 257(1), 202–206. LimCW WuBS A modified procedure for certain non-linear oscillators Journal of Sound and Vibration 2002 257 1 202 206 10.1006/jsvi.2001.4233 Search in Google Scholar

Hu H and Tang JH, Solutions of Duffing-harmonic oscillator by the method of Harmonic Balance, Journal of Sound and Vibration, 2006; 294(3):637–639. HuH TangJH Solutions of Duffing-harmonic oscillator by the method of Harmonic Balance Journal of Sound and Vibration 2006 294 3 637 639 10.1016/j.jsv.2005.12.025 Search in Google Scholar

Mickens RE, Harmonic Balance and Iterative calculations of periodic solutions to, J. Journal of Sound and Vibration, 2007; 306:968–972. MickensRE Harmonic Balance and Iterative calculations of periodic solutions to, J Journal of Sound and Vibration 2007 306 968 972 10.1016/j.jsv.2007.06.010 Search in Google Scholar

Hosen MA, Accurate approximate analytical solutions to an anti-symmetric quadratic nonlinear oscillator, African Journal of Mathematics and Computer Science Research, 2013; 6(5):77–81. HosenMA Accurate approximate analytical solutions to an anti-symmetric quadratic nonlinear oscillator African Journal of Mathematics and Computer Science Research 2013 6 5 77 81 Search in Google Scholar

Belendez A, Gimeno E, Alvarez ML and Mendez DI, Nonlinear oscillator with discontinuity by generalized Harmonic Balanced method, J. Computers and Math. with App., 2009; 58: 2117–2123. BelendezA GimenoE AlvarezML MendezDI Nonlinear oscillator with discontinuity by generalized Harmonic Balanced method J. Computers and Math. with App. 2009 58 2117 2123 10.1016/j.camwa.2009.03.004 Search in Google Scholar

Mickens RE, Iterative Procedure for determining approximate solutions to nonlinear oscillator equation, Journal of Sound and Vibration, 1987; 116: 185–188. MickensRE Iterative Procedure for determining approximate solutions to nonlinear oscillator equation Journal of Sound and Vibration 1987 116 185 188 10.1016/S0022-460X(87)81330-5 Search in Google Scholar

Mickens RE, A general procedure for calculating approximation to periodic solutions of truly nonlinear oscillators, Journal of Sound and Vibration, 2005; 287:1045–1051. MickensRE A general procedure for calculating approximation to periodic solutions of truly nonlinear oscillators Journal of Sound and Vibration 2005 287 1045 1051 10.1016/j.jsv.2005.03.005 Search in Google Scholar

Hu H, Solutions of a quadratic nonlinear oscillator: Iterative procedure, Journal of Sound and Vibration, 2006; 298:1159–1165. HuH Solutions of a quadratic nonlinear oscillator: Iterative procedure Journal of Sound and Vibration 2006 298 1159 1165 10.1016/j.jsv.2006.06.005 Search in Google Scholar

Chen YM and Liu JK, A modified Mickens Iterative procedure for nonlinear oscillators, Journal of Sound and Vibration, 2008; 314:465–473. ChenYM LiuJK A modified Mickens Iterative procedure for nonlinear oscillators Journal of Sound and Vibration 2008 314 465 473 10.1016/j.jsv.2008.03.007 Search in Google Scholar

Mickens R E, Truly Nonlinear Oscillations, 1st ed. World Scientific, Singapore, 2010. MickensR E Truly Nonlinear Oscillations 1st ed World Scientific Singapore 2010 10.1142/7561 Search in Google Scholar

Haque BI, Alam MS and Majedur RM, Modified solutions of some oscillators by Iterative procedure, Journal of the Egyptian Mathematical Society, 2013; 21:68–73. HaqueBI AlamMS MajedurRM Modified solutions of some oscillators by Iterative procedure Journal of the Egyptian Mathematical Society 2013 21 68 73 10.1016/j.joems.2013.02.003 Search in Google Scholar

Haque BI, A New Approach of Iterative Method for solving Some Nonlinear Jerk Equations, Global Journal of Science Frontier Research: F Mathematics & Decision Sciences, 2013; 13:87–98. HaqueBI A New Approach of Iterative Method for solving Some Nonlinear Jerk Equations Global Journal of Science Frontier Research: F Mathematics & Decision Sciences 2013 13 87 98 Search in Google Scholar

Haque BI, A new approach of modified Mickens Iterative method for solving some nonlinear jerk equations, British journal of Mathematics & Computer Science, 2014; 4(22):3146–3162. HaqueBI A new approach of modified Mickens Iterative method for solving some nonlinear jerk equations British journal of Mathematics & Computer Science 2014 4 22 3146 3162 10.9734/BJMCS/2014/11700 Search in Google Scholar

Haque B M I, Alam M S, Rahman M and Yeasmin I A, Iterative technique of periodic solutions to a class of non-linear conservative systems, Int. J. Conceptions on Computation and Information technology, 2014; 2(1):92–97. HaqueB M I AlamM S RahmanM YeasminI A Iterative technique of periodic solutions to a class of non-linear conservative systems Int. J. Conceptions on Computation and Information technology 2014 2 1 92 97 Search in Google Scholar

Haque BI and Hossain MR, An Analytic Solution of the Quadratic Nonlinear Oscillator by an Iterative Method, British journal of Mathematics & Computer Science, 2016; 13(1):3146–3162. HaqueBI HossainMR An Analytic Solution of the Quadratic Nonlinear Oscillator by an Iterative Method British journal of Mathematics & Computer Science 2016 13 1 3146 3162 10.9734/BJMCS/2016/22049 Search in Google Scholar

Haque BI, Bostami MB, Hossain MA, Hossain MR and Rahman MM, Mickens Iterative Like Method for Approximate Solutions of the Inverse Cubic Truly Nonlinear Oscillator, British journal of Mathematics & Computer Science, 2016; 13(4):1–7. HaqueBI BostamiMB HossainMA HossainMR RahmanMM Mickens Iterative Like Method for Approximate Solutions of the Inverse Cubic Truly Nonlinear Oscillator British journal of Mathematics & Computer Science 2016 13 4 1 7 10.9734/BJMCS/2016/22823 Search in Google Scholar

Haque BI, Hossain MA, Bostami MB and Hossain MR, Analytical Approximate Solutions to the Nonlinear Singular Oscillator: An Iterative Procedure, British journal of Mathematics & Computer Science, 2016; 14(3):1–9. HaqueBI HossainMA BostamiMB HossainMR Analytical Approximate Solutions to the Nonlinear Singular Oscillator: An Iterative Procedure British journal of Mathematics & Computer Science 2016 14 3 1 9 10.9734/BJMCS/2016/23263 Search in Google Scholar

Haque BI, Assifuzzaman MD and Hasan MK, Improvement of analytical solution to the inverse truly nonlinear oscillator by Extended Iterative method, Communications in Computer and Information Science, 2017; 655:412–421. HaqueBI AssifuzzamanMD HasanMK Improvement of analytical solution to the inverse truly nonlinear oscillator by Extended Iterative method Communications in Computer and Information Science 2017 655 412 421 10.1007/978-981-10-4642-1_35 Search in Google Scholar

Haque BI, Reza AS and Rahman MM, On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method, Journal of Advances in Mathematics and Computer Science, 2019; 33(3):1–9. HaqueBI RezaAS RahmanMM On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method Journal of Advances in Mathematics and Computer Science 2019 33 3 1 9 10.9734/jamcs/2019/v33i330177 Search in Google Scholar

Taylor AE and Mann WR, Advance Calculus, 1st ed. Wiley, New York, 1983. TaylorAE MannWR Advance Calculus 1st ed Wiley New York 1983 Search in Google Scholar

Gottlieb HPW, Harmonic balance approach to periodic solutions of nonlinear jerk equation, Journal of Sound and Vibration, 2004; 271:671–683. GottliebHPW Harmonic balance approach to periodic solutions of nonlinear jerk equation Journal of Sound and Vibration 2004 271 671 683 10.1016/S0022-460X(03)00299-2 Search in Google Scholar

eISSN:
2444-8656
Langue:
Anglais
Périodicité:
Volume Open
Sujets de la revue:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics