Squarification of telescope matrices in the probabilistic evolution theoretical approach to the two particle classical mechanics as an illustrative implementation

Abstract

In this work, the use of probabilistic evolution theory for the solution of two particle classical mechanics problem is under consideration. Using the separation of the mass center and some algebra, it is possible to reduce the problem to the solution of the initial value problem which has two differential equations and two unknown functions. This is the starting point of this manuscript and the steps up to this point is given in a companion paper. Then, space extension, constancy adding space extension, probabilistic evolution theory with squarification are utilized to form a numerical approximation. These steps and the results are detailed. Therefore, a complete application of probabilistic evolution theory is provided and the results are compared to the results obtained by fourth order Runge-Kutta method.