Variational Iterative Method Applied to Variational Problems with Moving Boundaries

Abstract

In this paper, He’s variational iterative method has been applied to give exact solution of the Euler Lagrange equation which arises from the variational problems with moving boundaries and isoperimetric problems. In this method, general Lagrange multipliers are introduced to construct correction functional for the variational problems. The initial approximations can be freely chosen with possible unknown constant, which can be determined by imposing the boundary conditions. Illustrative examples have been presented to demonstrate the efficiency and applicability of the variational iterative method.

In this paper, He’s variational iterative method has been applied to give exact solution of the Euler Lagrange equation which arises from the variational problems with moving boundaries and isoperimetric problems. In this method, general Lagrange multipliers are introduced to construct correction functional for the variational problems. The initial approximations can be freely chosen with possible unknown constant, which can be determined by imposing the boundary conditions. Illustrative examples have been presented to demonstrate the efficiency and applicability of the variational iterative method.

Keywords

Variational Iterative Method; Variational Problems; Moving Boundaries; Isoperimetric Problems

Variational Iterative Method; Variational Problems; Moving Boundaries; Isoperimetric Problems

Cite this paper

F. Ghomanjani and S. Ghaderi, "Variational Iterative Method Applied to Variational Problems with Moving Boundaries,"*Applied Mathematics*, Vol. 3 No. 5, 2012, pp. 395-402. doi: 10.4236/am.2012.35061.

F. Ghomanjani and S. Ghaderi, "Variational Iterative Method Applied to Variational Problems with Moving Boundaries,"

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