Simple yet efficient Newton-like method for systems of nonlinear equations

Abstract

We present a three-step iterative method of convergence order five for solving systems of nonlinear equations. The methodology is based on Newton's and Newton-like iterations. Hence, the name Newton-like method. Computational efficiency of the new method is considered and compared with well-known existing methods. Numerical tests are performed on some problems of different nature, which confirm robust and efficient convergence behavior of the proposed technique. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the numerical problems. It is shown that, in general, the new method is more efficient than the existing counterparts.