MA
–
202
Numerical Methods in Engineering
Assignment # 4
(Due by: Friday, February 14
th
2014)
1.
Use the Trapezoidal rule to obtain the approximate value
for n=1, 2, 4 of the following
integral (n represents number of segments/intervals): (10 Marks)
∫
2.
Use
Simpson’s 1/3 and 3/8 rules to find the integral given in the problem 1.
(10 Marks)
3.
Degree of Precision: Let
I
n
be a quadrature rule, and assume it is exact for all polynomials of
degree
≤ p
. Then we say that
I
n
has degree of precision
p
. You can find degree of precision of a
quadrature rule by calculating integrals of
p+1
monomials as follows:
e.g.
The 2-point Gauss Legendre formula given by
(
√
) (
√
)
has degree of
precision
p=3
as it will give exact results for monomials:
.
Now calculate the degree of precision of the following quadrature formula: (10 Marks)
∫
4.
The quadrature formula
∫
is exact for all polynomials of
degree less than or equal to 2. Determine
c
0
, c
1
and
c
2
. What is the degree of precision of this
formula? (10 Marks)
5.
Bound the error in
This preview has intentionally blurred sections.
Sign up to view the full version.
This is the end of the preview.
Sign up
to
access the rest of the document.
