Fourth-order variants of Cauchy’s method for solving non-linear equations

摘要

In this paper, we present some new variants of Cauchy’s method, in which the second derivative is replaced by a finite difference between the first derivatives. Analysis of convergence shows that the new methods have fourth-order convergence. Per iteration the new methods require one evaluations of the function and two of its first derivative. Numerical results show that the new methods are efficient.