Accès libre

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

B. M. Ikramul Haque
B. M. Ikramul Haque
 et 
Shajia Afrin Flora
Shajia Afrin Flora
   | 15 juin 2020
Applied Mathematics and Nonlinear Sciences's Cover Image
À propos de cet article
Article précédent
Article suivant
Citez
Publié en ligne: 15 juin 2020
Pages: 527 - 536
Reçu: 30 sept. 2019
Accepté: 23 déc. 2019
DOI: https://doi.org/10.2478/amns.2020.2.00008
Mots clés
© 2020 B. M. Ikramul Haque et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Adopted approximate frequencies of x¨+x2=0 \ddot x + {x^2} = 0 .

Exact frequency Ωe=0.914681A {\Omega _e} = 0.914681\sqrt A
Amplitude A
First approximate frequencies, Ω0 0.921318A 0.921318\sqrt A Second approximate frequencies, Ω1 0.914752A 0.914752\sqrt A Third approximate frequencies, Ω2 0.91467A 0.91467\sqrt A
Error (%) 0.73 Error (%) 0.0078 Error (%) 0.0012

Comparison of the approximate frequencies with exact frequency Ωe of x¨+x2=0 \ddot x + {x^2} = 0 .

Exact frequency Ωe=0.914681A {\Omega _e} = 0.914681\sqrt A
Amplitude A First approximate frequencies, Ω0 & Error (%) Second approximate frequencies, Ω1 & Error (%) Third approximate frequencies, Ω2 & Error (%)
Mickens and Ramadhani [9] 0.921318A 0.73 0.921318\sqrt A \,0.73  0.914044A 0.70 0.914044\sqrt A 0.70 –
Belendez et al. [14] 0.921318A 0.73 0.921318\sqrt A \,0.73 0.914274A 0.045 0.914274\sqrt A \,0.045  0.914711A 0.0032 0.914711\sqrt A \,0.0032
Hosen M A [13] 0.921318A 0.73 0.921318\sqrt A \,0.73 0.914427A 0.028 0.914427\sqrt A \,0.028  0.914733A 0.0056 0.914733\sqrt A \,0.0056
Haque and Hossain [24] 0.921318A 0.73 0.921318\sqrt A \,0.73 0.915114A 0.047 0.915114\sqrt A \,0.047  0.914705A 0.0026 0.914705\sqrt A \,0.0026
Adopted method 0.921318A 0.73 0.921318\sqrt A \,0.73  0.914752A 0.0078 0.914752\sqrt A \,0.0078  0.91467A 0.0012 0.91467\sqrt A \,0.0012

Comparison of the approximate periods with exact periods Te of x¨+x=−xx˙2 \ddot x + x = - x{\dot x^2} .

A Te T Er(%) TG Er(%)
0.1 6.275334 6.275333 3.43 e−6 6.2753264 1.21 e−4
0.2 6.251809 6.251809 3.61 e−7 6.251690 1.90 e−3
0.5 6.088449 6.088449 3.01 e−6 6.083668 7.85 e−2
1 5.527200 5.527434 4.25 e−3 5.441398 1.55
1.5 4.690247 4.709049 4.7 e−1 4.155936 11.39
eISSN:
2444-8656
Langue:
Anglais
Périodicité:
Volume Open
Sujets de la revue:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics
RSS Feed de la revue