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
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