An approximate solution treatment for non-linear problems

Abstract

In this paper, we study one-simple, typical non-linear equation to describe a kind of analytical technique for non-linear problems. This technique is based on both homotopy in topology and the Maclaurin series. In contrast to perturbation techniques, the homotopy technique does not require small or large parameters. The results show that the homotopy technique can give much better approximation than given by perturbation techniques. In addition the homotopy technique can be used to obtain formula uniformly valid for both small and large parameters in non-linear problems. It is clear that the homotopy technique is suitable for strongly non-linear problems.