A new iterative linearization approach for solving nonlinear equations systems

Abstract

Nonlinear equations arise frequently while modeling chemistry, physics, economy and engineering problems. In this paper, a new iterative approach for finding a solution of a nonlinear equations system (NLES) is presented by applying a linearization technique. The proposed approach is based on computational method that converts NLES into a linear equations system by using Taylor series expansion at the chosen arbitrary nonnegative initial point. Using the obtained solution of the linear equations system, a linear programming (LP) problem is constructed by considering the equations as constraints and minimizing the objective function constructed as the summation of balancing variables. At the end of the presented algorithm, the exact solution of the NLES is obtained. The performance of the proposed approach has been demonstrated by considering different numerical examples from literature.

Efficient Family of Iterative Methods for Solving Nonlinear Simultaneous Equations: A Comparative Study

“…Different methods have different amenities and limitations [9,10]. While some methods give good accuracy but take a large number of iterations [24]. On the other hand, some methods provide high accuracy in short iteration numbers but the computational complexity is immense which takes huge time to compute [25,26,27].…”