Aydın, Tuba Ağırman; Sezer, Mehmet; (Mashiyev), Rabil Ayazoglu; Çayan, Seda

The fixed-width curves, which have a very special place in many fields such as kinematics, engineering, art, cam design and geometry, are specially discussed under this title. In this study, three differential equations obtained by means of a system of differential equations characterizing fixed-width curves are examined. These differential equations are third order, variable coefficient, homogeneous, linear differential equations based on different variables. Approximate solutions of these equations are calculated with two different polynomial approximations and error analysis is made for the solutions. Thus, the best approach method is determined for the most accurate result. Also, these equations can constitute a characterization for different types of curves according to different frames in different spaces. Therefore, this study is important not only for this curve type but also for the geometry of all curves that can be expressed with similar equations.

İncele

Aydin, Tuba Aǧirman; Sezer, Mehmet; Kocayiǧit, Hüseyin

In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.

AtıfOpenAlex1

İncele

Aydın, Tuba Ağırman; Sezer, Mehmet

In this study, we considered an n th order linear differential equation with variable coefficients characterizing spherical curves according to Frenet frame in Euclidean n-Space E n . 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 presented 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.

İncele

Aydın, Tuba Ağırman; Sezer, Mehmet

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

AtıfOpenAlex1·TR Dizin1

İncele