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Variational iteration method for modified Camassa–Holm and Degasperis–Procesi equations
Author(s) -
Yıldırım Ahmet
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1154
Subject(s) - linearization , nonlinear system , mathematics , convergent series , series (stratigraphy) , iterative method , perturbation (astronomy) , mathematical analysis , mathematical optimization , physics , paleontology , quantum mechanics , biology , power series
In this paper, He's variational iteration method (VIM) is employed successfully for solving modified Camassa–Holm and Degasperis–Procesi equations. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions or the perturbation theory. The results show applicability, accuracy and efficiency of VIM in solving nonlinear differential equations with fully nonlinear dispersion term. It is predicted that VIM can be widely applied in science and engineering problems. Copyright © 2008 John Wiley & Sons, Ltd.