Assignment#4 - MA 202 Numerical Methods in Engineering...

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