652 publications from this institution
This paper shows that the Toda oscillator can be converted to a new Helmholtz-Fangzhu equation, which is solved by the homotopy perturbation method with three expansions. The solution, the negative frequency and the damping rate are expanded into power forms in the homotopy parameter, the solution process is given step by step, and the results are of high accuracy. This paper gives a general approach to damp vibrations with singular terms,especially to the Helmholtz-Fangzhu oscillator.
The Blasius' equation f″′ + ff″ 2 =0, with boundary conditions f(0) = f′(0)0, f′(+∞)=1 is studied in this paper. An approximate analytical solution is obtained via the variational iteration method. The comparison with Howarth's numerical solution reveals that the proposed method is of high accuracy.
