A new iterative linearization approach for solving nonlinear equations systems

Abstract

Nonlinear equations arise frequently while modeling chemistry, physics, econ-omy and engineering problems. In this paper, a new iterative approach forfinding a solution of a nonlinear equations system (NLES) is presented byapplying a linearization technique. The proposed approach is based on com-putational method that converts NLES into a linear equations system by usingTaylor series expansion at the chosen arbitrary nonnegative initial point. Us-ing the obtained solution of the linear equations system, a linear programming(LP) problem is constructed by considering the equations as constraints andminimizing the objective function constructed as the summation of balanc-ing variables. At the end of the presented algorithm, the exact solution ofthe NLES is obtained. The performance of the proposed approach has beendemonstrated by considering different numerical examples from literature.