A new approach to nonlinear partial differential equations. (English) Zbl 0923.35046

He, Jihuan

Commun. Nonlinear Sci. Numer. Simul. 2, No. 4, electronic paper No. 9 (1997).

Summary: A novel method called variational iteration method is proposed to solve nonlinear partial differential equations without linearization or small perturbations. In this method, a correction functional is constructed by a general Lagrange multiplier, which can be identified via variational theory. An analytical solution can be obtained from its trial function with possible unknown constants, which can be identified by imposing the boundary conditions, by successively iteration.

MSC:

35G20	Nonlinear higher-order PDEs
35A15	Variational methods applied to PDEs
35G30	Boundary value problems for nonlinear higher-order PDEs

Keywords:

nonlinear problems; variational iteration method