Global Error Minimization method for nonlinear oscillators with highly nonlinearity

Abstract

In this paper, we used Global Error Minimization (GEM)method for nonlinear oscillators. This method convert the nonlinear oscillators into an equivalent optimization problem to obtain an analytical solutio n 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 a pproximation 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 h as demonstrated the accuracy and efficiency of this method by solving some example. Example is given to illustrate the effectiveness and convenience of the method.