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

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.