CGN 3421
Computer Methods
Fall 2001
CGN 3421
lab7_cmf01.fm
page 1 of 2
Lab #7
Work by hand:
Applying root finding, integration and differentiation (Equations on back)
ROOTS:
Consider the following equation
between
There is one root in the range 1.5 to 1.5
a) Perform three
iterations of the bisection method
to guess the root.
use [1.5 1.5] as initial range
b) Perform three
iterations of the Newton Raphson method
to guess the root.
Use .75 as your initial guess.
c) Evaluate the error at the end of each iteration.
INTEGRATION:
Solve the following integration problems numerically ‘by hand’ using the methods requested in the table
exact answer = 0.84
Complete the table below
Derivatives
Find the derivative numerically for the equation
at x = 0
(ans:
)
Complete the table below:
OVER
method
number of segments (N)
248
Trapezoidal
Simpson’s
Gauss Quadrature
1seg =
2 seg =
method
1
.2
.01
.001
backward difference
forward difference
central difference
H Z
()
;:
±
:
²
Ō³
:
´
µ
µ
¶·¸
Z
¶·¸
≤≤
Ō
¶
²
π

Z
²
Ō
²

Z
F
GZR
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Long
 Numerical Analysis, Newton Raphson, Rootfinding algorithm, 2point Gauss quadrature, Newton Raphson Root

Click to edit the document details