Differential Equation Characterizing Spherical Curves in E n and Solution of This Equation

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.