A Numerical Solution of the Generalized Burgers-Huxley Equation

Year 2022, , 75 - 84, 28.02.2022

Gonca Çelikten , Adem Cankurt

https://doi.org/10.35414/akufemubid.1006385

Abstract

In this study numerical solutions of the generalized Burgers-Huxley equation are obtained utilizing a new approach: The Crank Nicolson logarithmic finite difference method (CN-LFDM). The effectiveness of the suggested method is demonstrated by a numerical example for various parameter cases. Presented tables demonstrate that the obtained results are in excellent agreement with the exact solutions and better than numerical results acquired by other methods in the literature. The method was analyzed with the von-Neumann stability analysis method and it was shown that the method was unconditionally stable.

Keywords

Crank Nicolson logarithmic finite difference method, Generalized Burgers-Huxley equation, von Neumann Stability analysis.

Genelleştirilmiş Burgers-Huxley Denkleminin Bir Sayısal Çözümü

Abstract

Bu çalışmada, genelleştirilmiş Burgers-Huxley denkleminin sayısal çözümleri yeni bir yaklaşım kullanılarak elde edilmiştir: Crank Nicolson logaritmik sonlu farklar yöntemi (CN-LSFY). Önerilen yöntemin etkinliği, çeşitli parametre durumları için sayısal bir örnekle gösterilmiştir. Sunulan tablolar, elde edilen sonuçların tam çözümlerle mükemmel bir uyum içinde olduğunu ve literatürdeki diğer yöntemlerle elde edilen sayısal sonuçlardan daha iyi olduğunu göstermektedir. Yöntem, von-Neumann kararlılık analizi yöntemi ile analiz edilmiş ve yöntemin koşulsuz kararlı olduğu gösterilmiştir.

Keywords

Crank Nicolson logaritmik sonlu fark yöntemi, Genelleştirilmiş Burgers-Huxley denklemi, von Neumann kararlılık analizi.

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