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Application of He’s variational iteration method to Helmholtz equation. (English) Zbl 1086.65113
Summary: We implement a new analytical technique, J. H. He’s variational iteration method [Varational iteration method – a kind of nonlinear analytical technique: Some examples. Int. J. Nonlinear Mech. 34, 699–708 (1999)] for solving the linear Helmholtz partial differential equation. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers in the functionals can be identified optimally via the variational theory. The initial approximations can be freely chosen with possible unknown constants, which can be determined by imposing the boundary/initial conditions. The results compare well with those obtained by the Adomian’s decomposition method.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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