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Application of modified wavelet and homotopy perturbation methods to nonlinear oscillation problems

M. Salai Mathi Selvi
M. Salai Mathi Selvi
 and 
L. Rajendran
L. Rajendran
   | Aug 23, 2019
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Published Online: Aug 23, 2019
Page range: 351 - 364
Received: Apr 03, 2019
Accepted: Jun 07, 2019
DOI: https://doi.org/10.2478/AMNS.2019.2.00030
Keywords
© 2019 Salai Mathi Selvi and L. Rajendran, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 Public License.

Fig. 1

(a–c) Comparison of CWM (Eq.(24), HPM (Eq.(25) and numerical method (MATLAB result) for various parameter values. Fig.1(a)l = 0.5 and μ = 0.01 Fig.1(b)l = 0.5 and μ = 0.1 Fig.1(c)l = 0.5 and μ = 1.
(a–c) Comparison of CWM (Eq.(24), HPM (Eq.(25) and numerical method (MATLAB result) for various parameter values. Fig.1(a)l = 0.5 and μ = 0.01 Fig.1(b)l = 0.5 and μ = 0.1 Fig.1(c)l = 0.5 and μ = 1.

Fig. 2

Plot of displacement and velocity for oscillator Eq. (26) with weak nonlinearity and small amplitude oscillations l = 1.1 and μ = 0.1.
Plot of displacement and velocity for oscillator Eq. (26) with weak nonlinearity and small amplitude oscillations l = 1.1 and μ = 0.1.

Fig. 3

Comparison of CWM (Eq. (34), HPM (Eq. (35) and numerical method (MATLAB result) for various parameter values. Fig. 3(a)l = 0.1, α = 1 and β = 0.5 Fig.3(b)l = 0.1, α = 1 and β = 2 Fig. 3(c)l = 0.1, α = 2 and β = 0.5.
Comparison of CWM (Eq. (34), HPM (Eq. (35) and numerical method (MATLAB result) for various parameter values. Fig. 3(a)l = 0.1, α = 1 and β = 0.5 Fig.3(b)l = 0.1, α = 1 and β = 2 Fig. 3(c)l = 0.1, α = 2 and β = 0.5.

Fig. 4

Plot of displacement and velocity for oscillator Eq. (36) with weak nonlinearity and small amplitude oscillations l = 0.1, α = 1, β = 2.
Plot of displacement and velocity for oscillator Eq. (36) with weak nonlinearity and small amplitude oscillations l = 0.1, α = 1, β = 2.

Fig. 5

Comparison of CWM (Eq. (44), HPM (Eq. (45) and numerical method (MATLAB result) for fixed parameter values l = 0.5, ς = 0.2.
Comparison of CWM (Eq. (44), HPM (Eq. (45) and numerical method (MATLAB result) for fixed parameter values l = 0.5, ς = 0.2.

Fig. 6

Plot of displacement and velocity for oscillator Eq. (46) with weak nonlinearity and small amplitude oscillations l = 0.5, ς = 0.2.
Plot of displacement and velocity for oscillator Eq. (46) with weak nonlinearity and small amplitude oscillations l = 0.5, ς = 0.2.
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