HE’S VARIATIONAL ITERATION METHOD FOR SOLVING MODELLING THE POLLUTION OF A SYSTEM OF LAKES

Year 2009, Issue: 018, 59 - 70, 15.04.2009

Mehmet Merdan

Abstract

In this papers,He’s variational iteration method(VIM) is implemented to for solving analytically systems of nonlinear ordinary differential equations such as modelling the pollution of a system of lakes. The proposed scheme is based on variational iteration method (VIM), Laplace transform and Padé approximants. The results to get the variational iteration method (VIM) are applied Padé approximants. Our proposed approach showed results to analytical solutions of nonlinear ordinary differential equation systems. The results are compared with the results obtained by MATLAB ode15s and the variational iteration method (VIM) are applied Padé approximants. Some plots are presented to show the reliability and simplicity of the methods.

Keywords

Padé approximants, Variational iteration method, Modelling the pollution of a system of lakes

GÖLLER SİSTEMİNİN KİRLİLİK MODELİNİN ÇÖZÜMÜ İÇİN HE’NİN VARYASYONEL İTERASYON YÖNTEMİNİN UYGULANMASI

Abstract

Bu çalışmada göller sisteminin kirlilik modeli gibi nonlineer adi diferensiyel denklem sisteminin analitik çözümü için He’nin varyasyonel iterasyon yöntemi uygulandı. Önerilen yaklaşım varyasyonel iterasyon yöntemi, Laplace dönüşümü ve Padé yaklaşımlarını baz almaktadır. Varyasyonel iterasyondan elde edilen sonuçlara Padé yaklaşımları uygulanmıştır. Önerdiğimiz yaklaşım ile nonlinear adi diferensiyel denklem sisteminin analitik çözümleri gösterildi. Matlab ode15s den elde edilen sonuçlar ile VIM’e Padé yaklaşımı uygulandıktan sonra elde edilen sonuçlar karşılaştırıldı. Yöntemlerin güvenilirliği ve basitliğini göstermek için bazı grafikler sunuldu

Keywords

Padé yaklaşımı, Varyasyonel iterasyon yöntemi, Göller sistemi için kirlilik modeli

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