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Journals / Universal Journal of Mathematics and Applications / 2022 / Cilt: 5 - Sayı: 3

Study on the Applications of Semi-Analytical Method for the Construction of Numerical Solutions of the Burgers' Equation

Mine BABAOĞLU
Pages
82–88
Publication Date
2022-09-30
DOI
—
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AI Summary & Key Takeaways

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

Nonlinear partial differential equations can be solved with the help of presented method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper explores, the Burgers' Equation which is the considerable partial differential equation that emerges in nonlinear science.
📊
Key Findings & Data:As a result of comparisons, it is demonstrated that the gained solutions are in excellent agreement.
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Conclusion & Impact:Nonlinear partial differential equations can be solved with the help of presented method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Burgers' Equation · Homotopy Analysis Method · Auxiliary parameter

Abstract

In the present paper explores, the Burgers' Equation which is the considerable partial differential equation that emerges in nonlinear science. Also, Homotopy Analysis Method (HAM) has been implemented to Burgers' equation with given initial conditions. The efficieny of the proposed method is analyzed by using some illustrative problems. We are compared approximate solutions acquired via HAM with the exact solutions. As a result of comparisons, it is demonstrated that the gained solutions are in excellent agreement. Additionally, 2D-3D graphs and tables of attained results are drawn by means of a ready-made package program. The recent obtained results denote that HAM is extremely efficient technique. Nonlinear partial differential equations can be solved with the help of presented method.

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Cite This Article

BABAOĞLU, M. (2022). Study on the Applications of Semi-Analytical Method for the Construction of Numerical Solutions of the Burgers' Equation. Universal Journal of Mathematics and Applications, Cilt: 5 - Sayı: 3, 82–88. https://ajindex.com/articles/819892

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