An approximation to the solution of telegraph equation by variational iteration method. (English) Zbl 1169.65335

Biazar, J.; Ebrahimi, H.; Ayati, Z.

Numer. Methods Partial Differ. Equations 25, No. 4, 797-801 (2009).

Summary: The variational iteration method (VIM) has been applied to solve many functional equations. In this article, this method is applied to obtain an approximate solution for the Telegraph equation. Some examples are presented to show the ability of the proposed method. The results of applying the VIM are exactly the same as those obtained by the Adomian decomposition method. It seems less computation is needed in the proposed method.

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L15	Initial value problems for second-order hyperbolic equations

Keywords:

variational iteration method; telegraph equation; Lagrange multiplier; restricted variation; numerical examples; comparison methods; Adomian decomposition method

References:

[1]	Biazar, An Approximation to the Solution of Telegraph Equation by Adomian decomposition method, International Mathematical Forum 2 pp 2231– (2007) · Zbl 1140.65356
[2]	Inokuti, Variational Method in the Mechanics of Solids pp 156– (1978)
[3]	He, A new approach to nonlinear partial differential equations, Commum. Nonlinear Sci. Numer. Simulation 2 pp 230– (1997) · Zbl 0923.35046
[4]	He, Variational iteration method a kind of non-linear analytical technique: some examples, International Journal of Non-Linear Mechanics 34 pp 699– (1999) · Zbl 1342.34005
[5]	He, Variational iteration method-Some recent results and new interpretations, Journal of Computational and Applied Mathematics 207 pp 3– (2007) · Zbl 1119.65049