Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2008.848.853KhatamiI.TolouN.MahmoudiJ.RezvaniM.5200885The present study is motivated by the desire to investigate
the analytical solutions of fully developed shock wave equation by the
implementation two new methods, called Homotopy Analysis Method (HAM)
and Variational Iteration Method (VIM). The HAM eliminated the classical
perturbation method problem, because of the existence a small parameter
in the equation. VIM is on of the most effective and convenient ones for
both linear and nonlinear equations. The obtained results from the proposed
approximate solutions have been compared and verified with those of Adomian`s
Decomposition Method (ADM) and the Runge-Kutta`s algorithm (RK). It shows
that the numerical results of these methods are the same; while HAM can
be much easier, more convenient and more efficient to approach such problems
in comparison to VIM and other Traditional methods.]]>Adomian, G.,1988Al-Khled, K.,1996Allan, F.M. and K. Al-Khaled, 2006Burden, R.L. and J.D. Faires,1993Chow, C.Y.,1979He, J.H.,1997He, J.H.,1998He, J.H.,1998He, J.H.,1999He, J.H.,2006Liao, S.J.,1992Liao, S.J., 1995Liao, S.J.,1997Liao, S.J., 1999Liao, S.J., 2003Liao, S., 2004Liao, S.J., 2005Olver, P.J., 1986Rogers, C. and W.F. Shadwich, 1982Smaller, J., 1983