Various approaches to solving nonlinear equations

TL;DR

This paper reviews various methods for solving nonlinear equations, including traditional and minimization-based approaches, highlighting their challenges and providing practical guidance through R examples.

Contribution

It offers a comparative overview of approaches to nonlinear equations and demonstrates their application with R, addressing efficiency and solution-finding concerns.

Findings

Different methods have varying success rates in solving nonlinear equations.

Minimization techniques can be used as alternative solutions.

Practical guidance with R helps in choosing appropriate methods.

Abstract

Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions using more general nonlinear least squares or function minimization techniques. There are concerns, nonetheless, that we may fail to find solutions, or that the process will be inefficient. Examples are presented with R with the goal of providing guidance on the solution of nonlinear equations problems.