文章基本信息

标题：Adomian decomposition method for solving initial value problems in vibration models
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作者：Sudi Mungkasi ; I Made Wicaksana Ekaputra
期刊名称：MATEC Web of Conferences
电子版ISSN：2261-236X
出版年度：2018
卷号：159
DOI：10.1051/matecconf/201815901014
语种：English
出版社：EDP Sciences
摘要：A number of engineering problems have second-order ordinary differential equations as their mathematical models. In practice, we may have a large scale problem with a large number of degrees of freedom, which must be solved accurately. Therefore, treating the mathematical model governing the problems correctly is required in order to get an accurate solution. In this work, we use Adomian decomposition method to solve vibration models in the forms of initial value problems of second-order ordinary differential equations. However, for problems involving an external source, the Adomian decomposition method may not lead to an accurate solution if the external source is not correctly treated. In this paper, we propose a strategy to treat the external source when we implement the Adomian decomposition method to solve initial value problems of second-order ordinary differential equations. Computational results show that our strategy is indeed effective. We obtain accurate solutions to the considered problems. Note that exact solutions are often not available, so they need to be approximated using some methods, such as the Adomian decomposition method.