Choice of an initial guess for Newton's method to solve nonlinear differential equations

Hayoung Choi, Sang Dong Kim, Byeong-Chun Shin

Abstract: A proper initial guess is critical for implementing Newton's iteration to approximate an exact solution of a nonlinear differential equation like the Navier-Stokes equations or magnetohydrodynamic equations. In this article, we will provide a theoretical criteria for the way of choosing an initial guess required for Newton's iteration for approximating an exact solution of a nonlinear differential equation.