Taylor-Matrix Collocation Method to Solution of Differential Equations Characterizing Spherical Curves in Euclidean 4-Space

Year 2019, Volume: 15 Issue: 1, 1 - 7, 22.03.2019

Tuba Ağırman Aydın Mehmet Sezer

https://doi.org/10.18466/cbayarfbe.416121

Abstract

In this study we consider a third order linear differential equation
with variable coefficients characterizing spherical curves according to Frenet
frame in Euclidean 4-Space . This equation whose coefficients are related to special function,
curvature and torsion, is satisfied by the position vector of any regular unit
velocity spherical curve. These type equations are generally impossible to
solve analytically and so, for approximate solution we present a numerical method
based on Taylor polynomials and collocations points by using initial
conditions. Our method reduces the solution of problem to the solution of a
system of algebraic equations and the approximate solution is obtained in terms
of Taylor polynomials.

Keywords

Curves in Euclidean Space, Spherical curves, Taylor matrix method, Frenet frame, Linear differential equations; Matrix and collocation method

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