Research on a Modified Newton-Type Method with Fifth-Order Convergence for Solving Nonlinear Equations with Application in Material Science

摘要

Numerical solution methods of nonlinear equation have very broad application prospect in materials science. In this paper, we present and analyze a fifth-order convergent method for solving nonlinear equations. The method is free from second derivatives and permits f(x)=0 at some iteration points. Several numerical tests demonstrate that the sixth-order method given in this paper is more efficient and performs better than classical Newton's method.