[4] S.E. Jones, Remarks on the perturbation process for certain conservative systems, Int. J. Non-Linear Mech., 13 (1978), 125-128.
[5] T.D. Burton, A perturbation method for certain nonlinear oscillators, Int. J. Non-Linear Mech., 19 (1984), 397-407.
[6] Y.K. Cheung, S.H. Chen, S.L. Lau,A modified Lindstedt-Poincare method for certain strongly nonlinear oscillators, Int. J. Non-Linear Mech., 26 (1991),
367-378.
[7] J.H. He, Homoptopy perturbation method for bifurcation and nonlinear problems, Int. J. Non-linear Sci. Numerical Simulation, 6 (2005), 207-208.
[8] B.S. Wu, C.W, Lim, Large amplitude nonlinear oscillations of a general conservative system, Int. J. Non-Linear Mech., 39 (2004), 859-807.
[9] M.S. Alam, M.E. Haque, M.B. Hossain, A new analytical technique to find periodic solutions of nonlinear systems, Int. J. Non-Linear Mech., 42 (2007),
1035-1045.
[10] J.H. He, Preliminary reports on the energy balance for nonlinear oscillations, Mechanics Research Communications, 29 (2002), 107-111.
[11] R.E. Mickens, Iteration procedure for determining approximate solutions to nonlinear oscillator equation, J. Sound Vib., 116 (1987), 185-188.
[12] G. Veronis, A note on the method of multiple time-scales, Q. Appl. Math., (1980), 363-368.
[13] T.D. Burton, Z. Rahman, On the multi-scale analysis of strongly non-linear forced oscillators, Int. J. Non-Linear Mech., 21 (1986), 135-146.
[14] M.S. Alam, I.A. Yeasmin, M.S. Ahamed, Generalization of the modified Lindstedt-Poincare method for solving some strongly nonlinear oscillators, Ain
Shams Engg. J., 10 (2019), 195-201.
[15] R. B. Dingle, Asymptotic expansions: Their derivation and interpretation, London Academic Press, (1973).
[16] E. J. Hinch, Perturbation methods, Cambridge University Press, (1991).
[17] F. Say, Optimal successive complementary expansion for singular differential equations, Math Meth Appl. Sci., (2020), 1-10.
[18] A. D. Dean, Exponential asymptotics and homoclinic snaking, Ph.D. Thesis, University of Nottingham, 2012.
[19] H. Poincare, Sur les integrales irr´eguli`eres, Acta Mathematica, 8 (1886), 295-344.
[20] V. Marinca, N. Herisanu, A modified iteration perturbation method for some nonlinear oscillation problems, Acta Mechanica, 184 (1-4) (2006), 231-242.
Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators
The modified Lindstedt-Poincare method has been extended to obtain a faster convergent solution of nonlinear oscillators. First of all a classical type Lindstedt-Poincare solution has been determined and then a conversion formula has been used to find the desired solution. The solution has been compared and justified by corresponding numerical solution.
[4] S.E. Jones, Remarks on the perturbation process for certain conservative systems, Int. J. Non-Linear Mech., 13 (1978), 125-128.
[5] T.D. Burton, A perturbation method for certain nonlinear oscillators, Int. J. Non-Linear Mech., 19 (1984), 397-407.
[6] Y.K. Cheung, S.H. Chen, S.L. Lau,A modified Lindstedt-Poincare method for certain strongly nonlinear oscillators, Int. J. Non-Linear Mech., 26 (1991),
367-378.
[7] J.H. He, Homoptopy perturbation method for bifurcation and nonlinear problems, Int. J. Non-linear Sci. Numerical Simulation, 6 (2005), 207-208.
[8] B.S. Wu, C.W, Lim, Large amplitude nonlinear oscillations of a general conservative system, Int. J. Non-Linear Mech., 39 (2004), 859-807.
[9] M.S. Alam, M.E. Haque, M.B. Hossain, A new analytical technique to find periodic solutions of nonlinear systems, Int. J. Non-Linear Mech., 42 (2007),
1035-1045.
[10] J.H. He, Preliminary reports on the energy balance for nonlinear oscillations, Mechanics Research Communications, 29 (2002), 107-111.
[11] R.E. Mickens, Iteration procedure for determining approximate solutions to nonlinear oscillator equation, J. Sound Vib., 116 (1987), 185-188.
[12] G. Veronis, A note on the method of multiple time-scales, Q. Appl. Math., (1980), 363-368.
[13] T.D. Burton, Z. Rahman, On the multi-scale analysis of strongly non-linear forced oscillators, Int. J. Non-Linear Mech., 21 (1986), 135-146.
[14] M.S. Alam, I.A. Yeasmin, M.S. Ahamed, Generalization of the modified Lindstedt-Poincare method for solving some strongly nonlinear oscillators, Ain
Shams Engg. J., 10 (2019), 195-201.
[15] R. B. Dingle, Asymptotic expansions: Their derivation and interpretation, London Academic Press, (1973).
[16] E. J. Hinch, Perturbation methods, Cambridge University Press, (1991).
[17] F. Say, Optimal successive complementary expansion for singular differential equations, Math Meth Appl. Sci., (2020), 1-10.
[18] A. D. Dean, Exponential asymptotics and homoclinic snaking, Ph.D. Thesis, University of Nottingham, 2012.
[19] H. Poincare, Sur les integrales irr´eguli`eres, Acta Mathematica, 8 (1886), 295-344.
[20] V. Marinca, N. Herisanu, A modified iteration perturbation method for some nonlinear oscillation problems, Acta Mechanica, 184 (1-4) (2006), 231-242.
Sharif, M. N., Alam, M. S., & Yeasmin, İ. A. (2020). Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators. Universal Journal of Mathematics and Applications, 3(2), 53-60. https://doi.org/10.32323/ujma.597667
AMA
Sharif MN, Alam MS, Yeasmin İA. Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators. Univ. J. Math. Appl. June 2020;3(2):53-60. doi:10.32323/ujma.597667
Chicago
Sharif, Md. Nazmul, M. S. Alam, and İ. A. Yeasmin. “Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators”. Universal Journal of Mathematics and Applications 3, no. 2 (June 2020): 53-60. https://doi.org/10.32323/ujma.597667.
EndNote
Sharif MN, Alam MS, Yeasmin İA (June 1, 2020) Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators. Universal Journal of Mathematics and Applications 3 2 53–60.
IEEE
M. N. Sharif, M. S. Alam, and İ. A. Yeasmin, “Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators”, Univ. J. Math. Appl., vol. 3, no. 2, pp. 53–60, 2020, doi: 10.32323/ujma.597667.
ISNAD
Sharif, Md. Nazmul et al. “Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators”. Universal Journal of Mathematics and Applications 3/2 (June 2020), 53-60. https://doi.org/10.32323/ujma.597667.
JAMA
Sharif MN, Alam MS, Yeasmin İA. Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators. Univ. J. Math. Appl. 2020;3:53–60.
MLA
Sharif, Md. Nazmul et al. “Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators”. Universal Journal of Mathematics and Applications, vol. 3, no. 2, 2020, pp. 53-60, doi:10.32323/ujma.597667.
Vancouver
Sharif MN, Alam MS, Yeasmin İA. Faster Convergent Modified Lindstedt-Poincare Solution of Nonlinear Oscillators. Univ. J. Math. Appl. 2020;3(2):53-60.