A coupling method of a homotopy technique and a perturbation technique for non-linear problems

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