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Application of He’s variational iteration method for solving nonlinear BBMB equations and free vibration of systems. (English) Zbl 1166.65389

Summary: A new analytical method called J. H. He’s variational iteration method (VIM) [Appl. Math. Comput. 114, No. 2–3, 115–123 (2000; Zbl 1027.34009)] is introduced to be applied to solve nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equations and free vibration of a nonlinear system having combined linear and nonlinear springs in series in this article. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers can be identified optimally via the variational theory. The results are compared with the results of the homotopy analysis method and also with the exact solution. He’s variational iteration method in this problem functions so better than the homotopy analysis method and exact solutions one of them in per section.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
70J30 Free motions in linear vibration theory

Citations:

Zbl 1027.34009
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Full Text: DOI

References:

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