APPLICATION OF IMPROVED AMPLITUDE-FREQUENCY FORMULATION TO NONLINEAR DIFFERENTIAL EQUATION OF MOTION EQUATIONS
APPLICATION OF IMPROVED AMPLITUDE-FREQUENCY FORMULATION TO NONLINEAR DIFFERENTIAL EQUATION OF MOTION EQUATIONS
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DOI：
10.1142/s0217984909021466
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发表时间：
2009-11
影响因子：
1.9
通讯作者：
A. G. Davodi;D. Ganji;R. Azami;H. Babazadeh
中科院分区：
文献类型：
--
作者：
A. G. Davodi;D. Ganji;R. Azami;H. Babazadeh
本文提出了一种求解强非线性振子精确近似解析解的方法，称为改进的幅频公式。为了说明该方法的准确性，我们还用He的能量平衡法求解方程组，并将结果进行了比较。新的算法提供了有前途的方法，这是有用的非线性振荡。我们发现，这些获得的解决方案不仅受益于高精度，但也是一致有效的，在整个解决方案域，这是如此简单和有效。所研究的方程是相对论振子的一般运动方程和无量纲非线性运动微分方程，它们的解可以帮助研究人员将这种能力扩展到其他工作中。
This paper presents an approach for solving accurate approximate analytical solutions for strong nonlinear oscillators called improved amplitude-frequency formulation. For illustrating the accuracy of the method, we also solved equations with He's energy balance method and compared results. New algorithms offer promising approaches, which are useful for nonlinear oscillations. We find that these attained solutions not only benefit from a high degree of accuracy, but are also uniformly valid in the whole solution domain which is so simple to do and effective. The studied equations are the general motion equation and the non-dimensional nonlinear differential equation of motion for the relativistic oscillator, which their solution can be useful for researchers to extend this ability into their other works.