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Название:
Critical re-examination of Adomian's decomposition and homotopy perturbation methods in nonlinear mechanic
Коллекция:
Международные конференции » Нелинейная динамика
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Вид документа:
статья
Язык документа:
английский
Добавлен в архив:
03.12.2013
Сводная информация по документу:
Andrianov, I.V. Critical re-examination of Adomian's decomposition and homotopy perturbation methods in nonlinear mechanic [Текст] / Andrianov I.V., Olevs’kyy V.I. // Международные конференции : Нелинейная динамика - НТУ "ХПИ", 2010.
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This paper was provides a systematic account of Adomian’s decomposition method and the homotopy perturbation method from the standpoint of the theory of expansion in parameter for an approximate analytical integration of systems of equations in nonlinear dynamics. It was shown that approximations which have got by using those methods represent the expansions of the exact solution in the form of the Taylor series for the independent variable. A modified method of the continuation parameter is proposed, which combines both approaches. The method allows simplifying the calculations, both at the model building phase, and for its further use. Two-dimensional approximation was used of Padé type, which has shown its effectiveness for acceleration of approximations convergence and their analytic continuation. On the basis of the proposed method it was calculated solution for Riccati equation of special type, which is widely used in theory of solitons


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