ABSTRACT
This chapter discusses the numerical methods for solving a single nonlinear equation. Solution to nonlinear algebraic equations requires iterative numerical techniques to be used. Newton-Raphson or related methods are arguably the most widely used methods for solving nonlinear equations. The five numerical methods considered in the chapter—bisection, secant, regula falsi, fixed point iteration, and Newton-Raphson—were analyzed for their error behavior. Derivation of a general Newton-Raphson method uses multivariate Taylor's series expansion. The issue of poor global convergence is a major problem for Newton-Raphson method. The chapter explores some heuristic ways to improve the performance of Newton-Raphson. MATLAB solvers for nonlinear algebraic equations are provided in the Optimization Toolbox and are not available in the base MATLAB package. The chapter also discusses two MATLAB methods, fzero and fsolve, to solve single-variable and multivariable nonlinear equation problems, respectively.
