AN APPROXIMATE SOLUTION FOR LORENTZIAN SPHERICAL TIMELIKE CURVES

In this article, the differential equation of lorentzian spherical timelike curves is obtained in E-1(4). It is seen that the differential equation characterizing Lorentzian spherical timelike curves is equivalent to a linear, third order, differential equation with variable coefficients. It is impossible to solve these equations analytically. In this article, a new numerical technique based on hermite polynomials is presented using the initial conditions for the approximate solution. This method is called the modified hermite matrix-collocation method. With this technique, the solution of the problem is reduced to the solution of an algebraic equation system and the approximate solution is obtained. In addition, the validity and applicability of the technique is explained by a sample application.