A GALERKIN-LIKE SCHEME TO DETERMINE CURVES OF CONSTANT BREADTH IN EUCLIDEAN 3-SPACE

The main focus of this study is to obtain the approximate solutions of a first order linear differential equation system characterizing curves of constant breadth in Euclidean 3-space. For this purpose, we outline a polynomial-based method reminiscent of the Galerkin method. Considering the approxim...

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Published inTWMS journal of applied and engineering mathematics Vol. 11; no. 3; p. 646
Main Authors Yuzbasi, S, Karacayir, M
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.07.2021
Elman Hasanoglu
Subjects
Approximation
Curves
Differential equations
Error correction
Error reduction
Euclidean geometry
Galerkin method
Mathematical analysis
Mathematics
Polynomials
Online AccessGet full text
ISSN2146-1147
2146-1147

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Abstract The main focus of this study is to obtain the approximate solutions of a first order linear differential equation system characterizing curves of constant breadth in Euclidean 3-space. For this purpose, we outline a polynomial-based method reminiscent of the Galerkin method. Considering the approximate solutions in the form of polynomials, we obtain some relations, which then give rise to a linear system of algebraic equations. The solution of this system gives the approximate solutions of the problem. Additionally, the technique of residual correction, which aims to reduce the error of the approximate solution by estimating this error, is discussed in some detail. The method and the residual correction technique are illustrated with three examples.
AbstractList The main focus of this study is to obtain the approximate solutions of a first order linear differential equation system characterizing curves of constant breadth in Euclidean 3-space. For this purpose, we outline a polynomial-based method reminiscent of the Galerkin method. Considering the approximate solutions in the form of polynomials, we obtain some relations, which then give rise to a linear system of algebraic equations. The solution of this system gives the approximate solutions of the problem. Additionally, the technique of residual correction, which aims to reduce the error of the approximate solution by estimating this error, is discussed in some detail. The method and the residual correction technique are illustrated with three examples.
The main focus of this study is to obtain the approximate solutions of a first order linear differential equation system characterizing curves of constant breadth in Euclidean 3-space. For this purpose, we outline a polynomial-based method reminiscent of the Galerkin method. Considering the approximate solutions in the form of polynomials, we obtain some relations, which then give rise to a linear system of algebraic equations. The solution of this system gives the approximate solutions of the problem. Additionally, the technique of residual correction, which aims to reduce the error of the approximate solution by estimating this error, is discussed in some detail. The method and the residual correction technique are illustrated with three examples. Keywords: Curves of constant breadth, systems of linear differential equations, Galerkin method, residual correction, numerical solutions. AMS Subject Classification: 34K28.
Audience Academic
Author Yuzbasi, S
Karacayir, M
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Copyright COPYRIGHT 2021 Turkic World Mathematical Society
2021. This work is licensed under http://creativecommons.org/licenses/by-nc/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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Elman Hasanoglu
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SubjectTerms Approximation
Curves
Differential equations
Error correction
Error reduction
Euclidean geometry
Galerkin method
Mathematical analysis
Mathematics
Polynomials
Title A GALERKIN-LIKE SCHEME TO DETERMINE CURVES OF CONSTANT BREADTH IN EUCLIDEAN 3-SPACE
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