Abstract
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.
Highlights
Vibration occurs in daily life, such as sounds, acoustics, machines, etc
We propose a computational treatment of the source term
We focus on solving the initial value problem (2) using the Adomian decomposition method
Summary
Vibration occurs in daily life, such as sounds, acoustics, machines, etc. A mathematical model for vibrations is the second-order ordinary differential equations. The model can be either with or without source terms. A number of researchers have attempted to solve vibration model, such as Nad [1], Ouyang and Zhang [2], and Supriyadi [3]. It is still an open problem about how to solve the model in an inexpensive computations. The Adomian decomposition method is chosen, as it has some advantages, such as that it is meshless, so solutions can be computed at any time [5,6]. We propose a computational treatment of the source term,.
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