A homotopy technique and a perturbation technique for non-linear problems

In this paper, a homotopy technique and a perturbation technique is proposed to solve non-linear problems. In constrast to the traditional perturbation methods, the homotopy method does not require a small parameter in the equation. In this method, according to the homotopy technique, a homotopy with an embedding parameter q ∈ [0, 1] is constructed, and the embedding parameter is considered as a small parameter. So that the homotpy techhnique can take full advantage of the traditional perturbation methods. Some applications are given. The results reveal that the new method is very effective and simple.