Adveksiyon ve reaksiyon terimlerinin varlığında uyumlu kesirli Cahn-Hilliard denkleminin yeni hibrit yöntemle yeni sayısal çözümleri

Yıl 2025, Cilt: 15 Sayı: 1, 274 - 285, 15.03.2025

Aslı Alkan , Hasan Bulut , Tolga Aktürk

Öz

Bu makalede, uyumlu kesirli Cahn-Hilliard denklemini analiz etmek için yeni sayısal yöntem kullanılmıştır. Cahn-Hilliard denklemi, matematiksel fizikte, özellikle çoklu fazlı sistemlerde spinodal ayrışma gibi faz ayırma olaylarını anlamak için önemli bir araç olarak kullanılan matematiksel bir modeldir. Bu çalışma, önerilen gelecekteki şemanın yakınsaklığını ve hatasını araştırmaktadır. Önerilen teknik, seri çözümünün yakınsama aralığını gösteren h-eğrileri üretir. Bu tekniğin etkinliğini ve uygunluğunu belirlemek için hata analizi gerçekleştirilmiştir. Ayrıca, çözümlerin 2B ve 3B grafikleri çizilmiştir. Ek olarak, grafiklerin davranışı yorumlanmıştır. Bu tekniğin basit, etkili ve hızlı olduğu gösterilmiştir.

Anahtar Kelimeler

Cahn-Hilliard denklemi, Shehu dönüşümü, Hata analizi

The novel numerical solutions of conformable fractional Cahn-Hilliard equation in the presence of advection and reaction terms via the novel hybrid method

Öz

In this paper, the novel numerical method is used to analyze the conformable fractional Cahn-Hilliard equation. The Cahn-Hilliard equation is a mathematical model employed as a crucial tool in mathematical physics, specifically for understanding phase separation phenomena such as spinodal decomposition in systems with multiple phases. This study investigates the convergence and error of the proposed future scheme. The proposed technique produces h-curves that show the series solution's convergence interval. To ascertain the efficacy and appropriateness of this technique, the error analysis has been conducted. Also, 2D and 3D graphs of the solutions were drawn. Additionally, the behavior of the graphs was commented. This technique has been shown to be simple, effective and fast.

Anahtar Kelimeler

Cahn-Hilliard equation, Shehu transform, Error analysis

Kaynakça

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