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A new approach to nonlinear partial differential equations. (English) Zbl 0923.35046
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:
35G20General theory of nonlinear higher-order PDE
35A15Variational methods (PDE)
35G30Boundary value problems for nonlinear higher-order PDE