**Author details**

In **Table 4**, the approximated computational order of convergence ACOC, the number of iterations, the difference between the two last iterations and the residual of the function at the last iteration are shown, for each one of the methods. In all cases, the initial estimation is a null

All the checked schemes provide the same solution of the nonlinear system. In **Table 4**, we can observe that all the fourth-order methods have a similar performance, but we note that the lowest error corresponds to method MA, duplicating the number of exact digits with respect

Many problems in science and engineering are modeled in such a way that, for their solution, it is necessary to solve systems of nonlinear equations. Therefore, designing iterative methods for solving these types of problems is an important task and it is a fruitful area of research. In this chapter, a review of the different techniques for constructing iterative methods is presented. Moreover, it is shown that real discrete dynamics tools are useful for analyzing the stability of the designed methods, selecting those with good dynamical behavior. In the numerical section, a chemical problem is used for testing the presented methods and the theoretical

This research was partially supported by Ministerio de Economía y Competitividad of Spain, MTM2014-52016-C2-2-P, and by Ministry of Higher Education Science and Technology of

( + 1) − () (()

)

vector and the Euclidean norm is used in the calculation of the residuals.

NM 1.9999 9 1.482e-413 6.448e-828 JM 3.9954 5 1.482e-413 1.976e-1007 OM 3.9964 5 1.482e-413 1.618e-1007 CM 3.9959 5 1.998e-353 1.618e-1007 MA 4.0519 5 5.362e-510 1.707e-2007 MB 3.9960 5 7.123e-362 1.409e-1449 MC 3.9960 5 3.110e-362 3.811e-1451

**Method ACOC Iteration**

112 Nonlinear Systems - Design, Analysis, Estimation and Control

to the other ones.

**5. Conclusions**

results are confirmed.

**Acknowledgements**

Dominican Republic, FONDOCYT 2014-1C1-088.

**Table 4.** Numerical results for molecular interaction problem.

Alicia Cordero1 , Juan R. Torregrosa1 and Maria P. Vassileva2\*

\*Address all correspondence to: maria.penkova@intec.edu.do

