The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. In computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient and iterative methods for finding the solutions of non-linear equations or variational inclusions are presented in this book. Also discussed herein is the study of applications of these methods in engineering and biosciences problems whose formulations are non-linear equations or variational inequalities.