Variational iteration method – a kind of non-linear analytical technique: Some examples. (English) Zbl 1342.34005

He, Ji-Huan

Int. J. Non-Linear Mech. 34, No. 4, 699-708 (1999).

Summary: In this paper, a new kind of analytical technique for a non-linear problem called the variational iteration method is described and used to give approximate solutions for some well-known non-linear problems. In this method, the problems are initially approximated with possible unknowns. Then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory. Being different from the other non-linear analytical methods, such as perturbation methods, this method does not depend on small parameters, such that it can find wide application in non-linear problems without linearization or small perturbations. Comparison with Adomian’s decomposition method reveals that the approximate solutions obtained by the proposed method converge to its exact solution faster than those of Adomian’s method.

MSC:

34A05	Explicit solutions, first integrals of ordinary differential equations
34C15	Nonlinear oscillations and coupled oscillators for ordinary differential equations

Keywords:

Variational iteration method; Duffing equation; Non-linear equations