Solving recent applications by quasi-Newton methods

In \cite{ros}, we have shown that there are many recent problems in applied research for which the quasi-Newton methods are the best option for solving the nonlinear systems of equations that appear in the solution of such problems. The main reason for using these methods is because they have low computational cost \cite{mar}, \cite{lop1}, \cite{lop}. Motivated by this work and by the fact that the ICUM, was considered recently as the most efficient quasi-Newton method for solving large-scale nonlinear systems \cite{luksan}, we are now interested in implementing it with some real problems.For this, we consider in this work four problems of common occurrence in applications in Geophysics, Biology, Engineering and Physics, respectively. Two of them are described here based in recent works \cite{carlos},\cite{sil}. The two other applications were described in \cite{ros} with base in \cite{med},\cite{mil}.For solving each problem, we must solve a nonlinear system of equations. For this, we use the quasi-Newton methods: Broyden and ICUM and present a careful comparative analysis of the results obtained.