A Galerkin-like scheme to determine curves of constant breadth in Euclidean 3-space

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.