Variational iteration and homotopy perturbation method for solving Lorenz system

Bu çalışmada, Lorenz sistemi gibi lineer olmayan adi diferensiyel denklem sistemlerinin yaklaşık analitik çözümlerini elde edebilmek için homotopy perturbation ve varyasyonel iterasyon yöntemleri uygulandı. Homotopy perturbation yöntemi varyasyonel iterasyon yöntemi ile mukayese edildi. Varyasyonel iterasyon yöntemi perturbation yöntemi olarak bilinen diğer non lineer yöntemlerden daha üstündür. VIM yönteminin temel özelliği lineer olmayan denklemleri doğru ve uygun çözebilecek esneklikte olmasıdır. Bu yöntemde genelde Lagrange çarpanları sistemler için düzeltme fonksiyoneli ile elde edildi. Çarpanlar varyasyonel teori ile belirlendi. VIM ve HPM yöntemlerini karşılaştırmak için bir kaç tane grafik sunuldu

In this paper, homotopy perturbation method and variational iteration method are implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as Lorenz system. Homotopy perturbation is compared the variational iteration method for Lorenz system. The variational iteration method is predominant than the other non-linear methods, such as perturbation method. The main property of the VIM method is in its flexibility and ability to solve nonlinear equations accurately and conveniently. In this method, in general Lagrange multipliers are constructed by correction functionals for the systems. Multipliers can be identified by the variational theory. Some plots are presented to compare of the VIM and HPM

Keywords:

Variational iteration method, Homotopy perturbation method Lorenz system,

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