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.
📌 3 Key Takeaways
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Objective & Hypothesis: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.
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Key Findings & Data: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.
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Conclusion & Impact: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.
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.
Özet
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.
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