HOMOTOPY PERTURBATION METHOD FOR SOLVING MODELLING THE POLLUTION OF A SYSTEM OF LAKES

Year 2009, Volume: 4 Issue: 1, 99 - 111, 08.06.2009

Mehmet Merdan

Abstract

Abstract: In this article, homotopy perturbation method is implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as modelling the pollution of a system of lakes. The proposed scheme is based on homotopy perturbation method (HPM), Laplace transform and Padé approximants. The results to get the homotopy perturbation method (HPM) are applied Padé approximants. The accuracy of this method is examined by comparison with the Matlab ode23s. Our proposed approach showed results to analytical solutions of nonlinear ordinary differential equation systems. Some plots are presented to show the reliability and simplicity of the methods.

Key words: Padé approximants, homotopy perturbation method, modelling the pollution of a system of lakes




BİR GÖLLER SİSTEMİNİN KİRLİLİK MODELİNİN HOMOTOPY PERTURBATİON YÖNTEMİ İLE ÇÖZÜMÜ

Özet: Bu makale de bir göller sisteminin kirlilik modeli gibi lineer olmayan adi diferensiyel denklem sisteminin yaklaşık analitik çözümünü bulmak için homotopy perturbation yöntemi uygulandı. Önerilen yöntem homotopy perturbation yöntemi, Laplace dönüşümü ve Padé yaklaşımını baz alır. Homotopy perturbation yöntemin'den elde edilen sonuçlara Padé yaklaşımı önerildi. Bu yöntemin doğruluğu Matlab ode23s ile mukayese edildi. Önerdiğimiz yaklaşım, lineer olmayan adi diferensiyel denklem sistemlerinin analitik çözümlerini gösterdi. Yöntemin güvenilirliğini ve basitliğini göstermek için bazı grafikler sunuldu.

Anahtar kelimeler: Padé yaklaşımı, Homotopy perturbation yöntemi, Bir göller sisteminin kirlilik modeli

Keywords

Padé yaklaşımı, Homotopy perturbation yöntemi, Bir göller sisteminin kirlilik modeli

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