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Journals / Turkish Journal of Mathematics and Computer Science / 2019 / Cilt: 11 - Sayı: 2

A Numerical Approach for Solving the System of Differential Equations Related to the Spherical Curves in Euclidean 3-Space

HÜseyin Kocayigit
Mehmet SEZER
Seda Çayan
Pages
84–96
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

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

In the present work, a) it is giventhe system of differential equations of the spherical curves in 3-dimensional Euclidean space; b) it is shown that thenumerical solutions of this system of differential equations are obtained in the truncated Taylor series form by usingTaylor matris collocation method; c) an example together with error analysis are given to demonstrate the validityand applicability of present method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In 1971, integral form of spherical curve in 3-dimensional Euclidean space was given in [3].
📊
Key Findings & Data:Theexplicit characterization of the spherical curves in n-dimensional Euclidean space was given in [12].
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Conclusion & Impact:In the present work, a) it is giventhe system of differential equations of the spherical curves in 3-dimensional Euclidean space; b) it is shown that thenumerical solutions of this system of differential equations are obtained in the truncated Taylor series form by usingTaylor matris collocation method; c) an example together with error analysis are given to demonstrate the validityand applicability of present method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In 1971, integral form of spherical curve in 3-dimensional Euclidean space was given in [3]. Theexplicit characterization of the spherical curves in n-dimensional Euclidean space was given in [12]. Morever, theposition vector of spherical curves in Euclidean 3-space was determined in [10]. In the present work, a) it is giventhe system of differential equations of the spherical curves in 3-dimensional Euclidean space; b) it is shown that thenumerical solutions of this system of differential equations are obtained in the truncated Taylor series form by usingTaylor matris collocation method; c) an example together with error analysis are given to demonstrate the validityand applicability of present method.

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Cite This Article

Kocayigit, H., SEZER, M., Çayan, S. (2022). A Numerical Approach for Solving the System of Differential Equations Related to the Spherical Curves in Euclidean 3-Space. Turkish Journal of Mathematics and Computer Science, Cilt: 11 - Sayı: 2, 84–96. https://ajindex.com/articles/609122

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References (15)

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