ABSTRACT
This chapter explains how to solve nonlinear systems of algebraic equations. Numerical methods are presented to find the solution of a single nonlinear equation, referred to as root finding. Numerical methods to solve simultaneous nonlinear equations are also presented. A nonlinear algebraic equation is typically impossible to solve explicitly. A few special cases, such as the quadratic equation, can be solved exactly, but these cases are the exception. The most widely used bracketing methods are the bisection method and the false position method. These are based on two initial guesses that bracket or surround the root. The bisection method is one type of incremental search methods where the interval containing the root is refined by dividing into halves and retaining the subinterval containing the root. This process is repeated until some desired accuracy criterion is met.
