ESCUELA DE INGENIERÍA DE PETROLEOS

RUBEN DARIO ARISMENDI RUEDA

ESCUELA DE INGENIERÍA DE PETROLEOS

CHAPTER 4: ‘ROOTS OF EQUATIONS’

ESCUELA DE INGENIERÍA DE PETROLEOS

The roots of equations are the values of x that makes f(x)=0. There are many forms to obtain this values of x, but the most common is the quadratic formula. The other forms are mostly numerical methods and graphical methods that are used when is not to easy to find the root of the function.

ESCUELA DE INGENIERÍA DE PETROLEOS

There are some different kind of methods to find the roots of Equation:

GRAPHICSOPEN

METHODSCLOSE

METHODS

FIXED POINT NEWTON-

RAPHSONSECANT FAKE

POSITIONBISECCION

ESCUELA DE INGENIERÍA DE PETROLEOS

http://s4.hubimg.com/u/351_f520.jpg

f(x)=0

ESCUELA DE INGENIERÍA DE PETROLEOS

CLOSE METHODS.

1. Biseccion

ESCUELA DE INGENIERÍA DE PETROLEOS

The objective of this Method consist in divide the interval to the half, looking forward for the change of sings.

If F(x) is Real and continous in the interval that goes from X(inf) to X(sup) and then there is at least 1 root

between the intervals

0)(.)( si xfxf)(),( si xx

ESCUELA DE INGENIERÍA DE PETROLEOS

2

sir

xxx

)(xf

ix sx HALFxr

ESCUELA DE INGENIERÍA DE PETROLEOS

0)(.)( ri xfxf

THE ROOT WILL BE IN THE Inf. SEGMENT SO:Xi= STILL THE SAMEXs= THE LAST Xr

0)(.)( ri xfxfTHE ROOT WILL BE IN THE Sup. SEGMENT SO:Xi= THE LAST XrXs= STILL THE SAME

ESCUELA DE INGENIERÍA DE PETROLEOS

Example

CALCULATE THE ROOT OF THE NEXT EQUATION.

%100actualr

anteriorr

actualr

a x

xxE

ERROR FOR THE NEW RESULT

ESCUELA DE INGENIERÍA DE PETROLEOS

In the table, we can see that the value in the 7th iteration is 0,42578125 which is approximate to the real value with an error of 0,00917431.