Root finding of a system of nonlinear equations using the combination of newton, conjugate gradient and quadrature methods

Abstract

A system of nonlinear equations is a well-known problem in many fields of science and engineering. There may have no solution or multiple solutions for the systems. This dissertation is aimed to solve a system of nonlinear equations using combination of Newton, conjugate gradient and quadrature methods. This new method is able to improve the approximated solution of a system of nonlinear equations. C++ compiler is used to achieve the objectives of this dissertation. Besides that, conjugate gradient method is used to find sufficiently accurate starting approximations for the Newton-based techniques. Three examples of system of nonlinear problems have been presented in this dissertation. With the help of C++ compiler, the numerical technique has been reviewed. On the other hand, this dissertation is intended to analyze the efficiency and effectiveness of these methods through numerical simulations. Numerical results show that these methods surpassed the other methods in both efficiency and effectiveness.