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Journals / Ordu Üniversitesi Bilim ve Teknoloji Dergisi / 2022 / Cilt: 12 - Sayı: 1

On Exact and Numerical Solutions to the Burgers' and Coupled Burgers' Equation

Burgers ve coupled Burgers denklemlerinin tam ve nümerik çözümleri üzerine

Mine BABAOĞLU
Pages
1–10
Publication Date
2022-06-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

According to the results, we have found out that our gained solutions convergence very speedily to the analytical solutions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, one dimensional Burgers' equation and coupled Burgers' equation are solved via Homotopy perturbation method (HPM).
📊
Key Findings & Data:Solutions two and three-dimensional graphics and tables of some obtained results are constructed with the help of the computational program in the Wolfram Mathematica.
💡
Conclusion & Impact:According to the results, we have found out that our gained solutions convergence very speedily to the analytical solutions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:bir boyutlu Burgers denklemi · Coupled Burgers denklemi · Homotopi pertürbasyon metodu

Abstract

In this work, one dimensional Burgers' equation and coupled Burgers' equation are solved via Homotopy perturbation method (HPM). Solutions two and three-dimensional graphics and tables of some obtained results are constructed with the help of the computational program in the Wolfram Mathematica. All the solutions found in this study validate the efficiency of the method. According to the results, we have found out that our gained solutions convergence very speedily to the analytical solutions. In conclusion, we can say that the present method can also be applied for the solutions of a wide range of nonlinear problems.

Özet

Bu çalışmada, bir boyutlu Burgers denklemi ve Burgers denklemler sistemi Homotopi pertürbasyon metodu (HPM) ile çözülmüştür. Elde edilen çözümlerin iki ve üç boyutlu grafikleri ve tabloları Mathematica hesaplama programı yardımıyla oluşturulmuştur. Bu çalışmada bulunan tüm çözümler metodun etkinliğini doğrulamaktadır. Sonuçlara göre, elde ettiğimiz çözümlerin analitik çözümlere çok hızlı bir şekilde yakınsadığı ortaya çıkarılmıştır. Sonuç olarak, sunulan metodun geniş aralıktaki lineer olmayan problemlerin çözümleri için uygulanabilir olduğunu ifade etmemiz mümkündür.

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Cite This Article

BABAOĞLU, M. (2022). On Exact and Numerical Solutions to the Burgers' and Coupled Burgers' Equation. Ordu Üniversitesi Bilim ve Teknoloji Dergisi, Cilt: 12 - Sayı: 1, 1–10. https://ajindex.com/articles/694600

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