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Analytical solution for nonlinear wave propagation in shallow media using the variational iteration method
(Taylor & Francis Ltd, 2012) Younesian, Davood; Askari, Hassan; Saadatnia, Zia; Yildirim, Ahmet
An analytical solution is presented for nonlinear surface wave propagation. A variational iteration method (VIM) was employed and time-dependent profiles of the surface elevation level and velocity obtained analytically for different initial conditions. It is shown that the VIM used here is a flexible and accurate approach and that it can rapidly converge to the same results obtained by the Adomian decomposition method.
Periodic Solutions for the Generalized Nonlinear Oscillators containing Fraction Order Elastic Force
(Walter De Gruyter Gmbh, 2010) Younesian, Davood; Askari, Hassan; Saadatnia, Zia; Yildirim, Ahmet
Approximate periodic solutions for a conservative nonlinear oscillator containing x(2(m-n)+1/2n+1) elastic force are analytically obtained in this paper. He's Energy Balance Method (HEBM) and He's Variational Approach (HVA) are adopted as the solution methods. Correlation between the approximate frequencies and periodic solutions with the exact ones are verified and discussed. Two special cases are evaluated