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

M. Salai Mathi Selvi

M. Salai Mathi Selvi

Academy of Maritime Education and Training (AMET), Deemed to be University, Department of MathematicsKanathur, India
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Selvi, M. Salai Mathi
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L. Rajendran

L. Rajendran

Academy of Maritime Education and Training (AMET), Deemed to be University, Department of MathematicsKanathur, India
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Rajendran, L.
  
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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