An acceleration of the continuous Newton’s method

Abstract In this work, we study some numerical properties of the continuous Newton’s method, the continuous version of the classical Newton’s method for solving nonlinear equations p ( z ) = 0 . In fact, continuous Newton’s method is an initial value problem whose solutions flow to a root of the equation. We show the influence of the multiplicity of the roots of the considered equation in the Jacobian matrix related to the problem. In addition, we study some modifications of the continuous Newton’s method that allow us to increase the velocity of the convergence of the solutions towards the roots of p ( z ) = 0 .