Solving the nonlinear equations by the Newton-homotopy continuation method with adjustable auxiliary homotopy function

摘要

In this paper, the concept of adjustable auxiliary homotopy function for the Newton-homotopy continuation method is presented. By means of adjusting the auxiliary function, we can solve the nonlinear equations and guarantee the solutions exactly without divergence rather than the traditional numerical methods such as the Newton–Raphson method and so on.