Lecture Note of

University of Babylon
College of Engineering
Department of Environmental Engineering
Engineering Analysis I (ENAN 103)








Solution of Nonlinear Equation

Undergraduate Leve, 3th Stage



Mr. Waleed Ali Tameemi
College of Engineering/ Babylon University
M.Sc. Civil Engineering/ the University of Kansas/ USA



2016-2017
Lecture Outline
Introduction
Closed Methods
Bisection Method
False-Point Position Method
Open Methods
Newton-Raphson Method
Secant Method
Summary















1.0 – Introduction
The root of an equation can be defined as the set of the independent values that satisfies the equation. Equations are being divided into:

Figure 1:Equation types.
Solutions of nonlinear equations will discuss in the following sections.

2.0 – Closed Methods
These methods are being used in calculating the roots of nonlinear equations. Two values of x (two roots) are assumed. One of the assumed roots shall give negative value and the other must produce positive value when it apply in the equation. In other words,
f(x_p )=y_p (x which may be ± gives positive y)
f(x_n )=y_n (x which may be ± gives negative y).