AN APPROXIMATE SOLUTION TECHNIQUE NOT DEPENDING ON SMALL PARAMETERS - A SPECIAL EXAMPLE

One simple, typical non-linear equation is used in this paper 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 proposed method does not require small or large parameters. The example shows that the proposed method can give much better approximations than those given by perturbation techniques. In addition the proposed method can be used to obtain formulae uniformly valid for both small and large parameters in non-linear problems.