ROOT FINDING FOR NONLINEAR EQUATIONS

Abstract

Nonlinear equations /systems appear in most science and engineering models. For example, when solving eigen value problems, optimization problems, differential equations, in circuit analysis, analysis of state equations for a real gas, in mechanical motions /oscillations, weather forecasting, integral equations, image processing and many other fields of engineering designing processes. Nonlinear systems /problems are difficult to solve manually but they occur naturally in fluid motions, heat transfer, wave motions, chemical reactions, etc. This study deals with construction of iterative methods for nonlinear root finding, applying Taylor’s series approximation of a nonlinear function f(x) combined with a new correction term in a quadratic or cubic model. Competent iterative algorithms of higher order were investigated. For test of convergence and efficiency, we applied basic theorems and solved some equations in C++.

Keywords – nonlinear equations, Taylor’s approximation, iterative algorithms for roots, error correction