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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Bibliographic Details
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
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Summary: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.
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ISSN:2146-1147
2146-1147