TY - JOUR
T1 - Effective approximate methods for strongly nonlinear differential equations with oscillations
AU - Alquran, Marwan
AU - Al-Khaled, Kamel
N1 - Funding Information:
The authors would like to thank the editor and the anonymous referees for their in-depth reading, criticisms, and insightful comments on an earlier version of this paper.
Publisher Copyright:
© 2012, Alquran and Al-Khaled; licensee Springer.
PY - 2012/12
Y1 - 2012/12
N2 - Purpose: This paper proposes the use of different analytical methods in obtaining approximate solutions for nonlinear differential equations with oscillations. Methods: Three methods are considered in this paper: Lindstedt-Poincare method, the Krylov-Bogoliubov first approximate method, and the differential transform method. Results: Figures that are given in this paper give a strong evidence that the proposed methods are effective in handling nonlinear differential equations with oscillations. Conclusions: This study reveals that the differential transform method provides a remarkable precision compared with other perturbation methods.
AB - Purpose: This paper proposes the use of different analytical methods in obtaining approximate solutions for nonlinear differential equations with oscillations. Methods: Three methods are considered in this paper: Lindstedt-Poincare method, the Krylov-Bogoliubov first approximate method, and the differential transform method. Results: Figures that are given in this paper give a strong evidence that the proposed methods are effective in handling nonlinear differential equations with oscillations. Conclusions: This study reveals that the differential transform method provides a remarkable precision compared with other perturbation methods.
KW - Differential transform method
KW - Krylov-Bogoliubov method
KW - Lindstedt-Poincare method
KW - Nonlinear oscillations
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U2 - 10.1186/2251-7456-6-32
DO - 10.1186/2251-7456-6-32
M3 - Article
AN - SCOPUS:84938676875
SN - 2008-1359
VL - 6
JO - Mathematical Sciences
JF - Mathematical Sciences
IS - 1
M1 - 32
ER -