Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: A review
M Bayat, I Pakar, G Domairry - Latin American Journal of Solids and …, 2012 - SciELO Brasil
This review features a survey of some recent developments in asymptotic techniques and
new developments, which are valid not only for weakly nonlinear equations, but also for …
new developments, which are valid not only for weakly nonlinear equations, but also for …
An algorithm for solving the fractional nonlinear Schrödinger equation by means of the homotopy perturbation method
A Yildirim - International Journal of Nonlinear Sciences and …, 2009 - degruyter.com
In this study, we present a framework to obtain analytical solutions to nonlinear fractional
Schrödinger equations. The homotopy perturbation method (HPM) is employed to derive …
Schrödinger equations. The homotopy perturbation method (HPM) is employed to derive …
Nonlinear oscillator with discontinuity by parameter-expansion method
The parameter-expansion method is applied to a nonlinear oscillator with discontinuity. One
iteration is sufficient to obtain a highly accurate solution, which is valid for the whole solution …
iteration is sufficient to obtain a highly accurate solution, which is valid for the whole solution …
He's homotopy perturbation method for solving the space-and time-fractional telegraph equations
A Yıldırım - International Journal of Computer Mathematics, 2010 - Taylor & Francis
In this study, homotopy perturbation method (HPM) is used to obtain analytic and
approximate solutions of the space-and time-fractional telegraph equations. The space-and …
approximate solutions of the space-and time-fractional telegraph equations. The space-and …
On the variational iteration method and other iterative techniques for nonlinear differential equations
JI Ramos - Applied Mathematics and Computation, 2008 - Elsevier
A variety of iterative methods for the solution of initial-and/or boundary-value problems in
ordinary and partial differential equations is presented. These iterative procedures provide …
ordinary and partial differential equations is presented. These iterative procedures provide …
[HTML][HTML] Application of He's homotopy perturbation method for solving the Cauchy reaction–diffusion problem
A Yıldırım - Computers & Mathematics with Applications, 2009 - Elsevier
In this paper, the solution of Cauchy reaction–diffusion problem is presented by means of
the homotopy perturbation method. Reaction–diffusion equations have special importance …
the homotopy perturbation method. Reaction–diffusion equations have special importance …
Oscillator with fraction order restoring force
L Cveticanin - Journal of Sound and Vibration, 2009 - Elsevier
In this paper a new analytical method for solving the differential equations which describe
the motion of the oscillator with fraction order elastic force is introduced. Using the first …
the motion of the oscillator with fraction order elastic force is introduced. Using the first …
Application of a modified He's homotopy perturbation method to obtain higher-order approximations of an x1/3 force nonlinear oscillator
A modified He's homotopy perturbation method (HHPM) is used to calculate the periodic
solutions of a conservative nonlinear oscillator for which the elastic force term is proportional …
solutions of a conservative nonlinear oscillator for which the elastic force term is proportional …
[HTML][HTML] Methods for solving singular perturbation problems arising in science and engineering
M Kumar - Mathematical and Computer Modelling, 2011 - Elsevier
Singular perturbation problems are of common occurrence in all branches of applied
mathematics and engineering. These problems are encountered in various fields such as …
mathematics and engineering. These problems are encountered in various fields such as …
Application of a modified He's homotopy perturbation method to obtain higher-order approximations to a nonlinear oscillator with discontinuities
A modified He's homotopy perturbation method is used to calculate the periodic solutions of
a nonlinear oscillator with discontinuities for which the elastic force term is proportional to …
a nonlinear oscillator with discontinuities for which the elastic force term is proportional to …