Methods for Solving Algebraic Equations and Their Systems

Abstract

This chapter presents some basic numerical techniques to solve nonlinear algebraic equations and systems of linear and nonlinear equations. For non-linear algebraic equations the bisection, false position, Newton, fixed point iteration and some hybrid methods are described. Application of these methods is shown for typical open channel problems, like computation of the normal depth, critical depths or the depth of water over sharp-crested weir. Next the standard methods of solution of the system of linear equations are presented. The last section of the chapter is devoted to the solution of systems of non-linear equations, including the Newton and Picard iterative methods.