New approaches to identification of the Lagrange multiplier in the variational iteration method

作者：Samaee S S^*; Yazdanpanah O; Ganji D D

来源：Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015, 37(3): 937-944.

DOI：10.1007/s40430-014-0214-3

• Solution differential equation
• Lagrange multipliers (lambda)
• Variational iteration method (VIM)
• Laplace method transform
• New methods

In this paper, new methods to obtain the Lagrange multiplier are presented. Differential equation consists of linear and nonlinear parts. We have infinite equations that the linear parts of them are different together then any of the equations have different Lagrange multipliers. In this article, steps of the proposed methods are fully described manually. In this paper, we show that the proposed methods attain precisely the Lagrange multipliers. Exact identification of Lagrange multipliers in the VIM is very important for obtaining highly accurate solutions; on the other hand, it is complicate to determine the multipliers for strongly nonlinear equations. Lagrange coefficient is a parameter that is used in VIM. Therefore, this study introduces a simple and efficient way to solve Lagrange coefficient. The results show that all three methods obtain the Lagrange coefficient without any errors and manually are solved easily.

• 出版日期2015-5