An approximate solution technique not depending on small parameters: A special example. (English) Zbl 0837.76073

Liao, Shijun

Int. J. Non-Linear Mech. 30, No. 3, 371-380 (1995).

Summary: One simple, typical nonlinear equation is used in this paper to describe a kind of analytical technique for nonlinear 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 approximation 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 nonlinear problems.

MSC:

76M99	Basic methods in fluid mechanics
34A45	Theoretical approximation of solutions to ordinary differential equations

Keywords:

nonlinear problems; homotopy; Maclaurin series