A Robust Fixed Point Method to Solve System of Nonlinear Equations

Abstract

Solving nonlinear partial differential equations requires addressing systems of nonlinear algebraic equations. In this article, we propose a new fixed-point method for solving these systems. We assume that the method is both fast and globally convergent. Additionally, this method can be accelerated using Aitken or Anderson acceleration techniques. Several numerical test cases are presented to illustrate the efficiency of the proposed method.