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Global Error Minimization method for nonlinear oscillators with highly nonlinearity |
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PP: 1557-1561 |
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Author(s) |
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Muhammad Aslam Noor,
Waseem Asghar Khan,
Muhammad Arif,
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Abstract |
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| In this paper, we used Global ErrorMinimization (GEM)method for nonlinear oscillators. This method convert the nonlinear
oscillators into an equivalent optimization problem to obtain an analytical solution of the problem. Approximate solution obtained by
GEM method is compared with the solution of He’s variational approach. We observe from the results that this method is very simple,
easy to apply, and gives a very good accuracy by using first-order approximation and simplest trial functions. Comparison made with
other known results show that new method provides a mathematical tool to the determination of limit cycles of more complex nonlinear
oscillators. This method is applied on nonlinear differential equations. It has demonstrated the accuracy and efficiency of this method
by solving some example. Example is given to illustrate the effectiveness and convenience of the method. |
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