Numerical Simulation of Diffusion Equation by Means of He's Variational Iteration Method and Adomian's Decomposition Method

Year 2010, Volume: 7 Issue: 1, 25 - 38, 01.02.2010

Hikmet Koyunbakan Emrah Yılmaz

Abstract

In this study, we obtain approximate solutions for diffusion equation on a finite
interval by the Adomian decomposition method (ADM) and variational iteration method
(VIM) for three cases and then the numerical results are compared. These results show
that the ADM leads to more accurate results, and they indicate that only a few terms are
sufficient to obtain accurate solutions.

Keywords

Diffusion operator, Adomian’s decomposition method, He’s variational iteration method

Numerical Simulation of Diffusion Equation by Means of He’s Variational Iteration Method and Adomian’s Decomposition Method

Abstract

Bu ¸calı¸smada, sonlu bir aralıkta ¨u¸c durumda dif¨uzyon denklemi i¸cin ADM ve VIM
y¨ontemleri kullanılarak yakla¸sık ¸c¨oz¨umler elde edilmi¸s ve bulunan bu ¸c¨oz¨umler kar¸sıla¸stırılmı¸stır. Elde edilen sonu¸clar ADM’nin daha etkili sonu¸clar verdi˘gini g¨ostermi¸stir. Sayısal
sonu¸clar, sadece birka¸c terimin tam ¸c¨oz¨umler elde etmek i¸cin yeterli oldu˘gunu g¨ostermi¸stir.

Keywords

Difüzyon operatorü, Adomian ayrışım metodu, He’nin varyasyonel iterasyon metodu

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