No abstract

The most famous classical variational principle is the so-called Brachistochrone problem. In this work, Homotopy perturbation method (HPM) is applied to the Brachistochrone problem that arises invariational problems. The results reveal the efficiency and the accuracy of the proposed method. Homotopy perturbation method yields solutions in convergent series forms with easy computation.

The Adomian's decomposition method, the Homotopy perturbation method, and lyapunov's method are three powerful methods which consider an approximate solution of linear and non-linear equations, as an infinite series. In this paper, we show that these three methods are equivalent in solving functional equations. To illustrate the capability and reliability of the methods two examples are provided. Numerical solutions obtained by these methods are compared with the exact solutions we see that usually converging to an exact solution.