# Numerical Methods MA2264 MJ2014 6th Semester Question Paper

Anna University Question Paper
B.E./B.Tech. DEGREE EXAMINATION, May /June 2014.
MA2264-Numerical Methods
Question Paper
Regulation 2008/2010

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PART A (10*2=20)

1. Evaluate 15 using Newton Raphins formula.
2. Using Dauss elimination method solve : 5x+4y=15,3x+7y=12.
3.Find the second divided difference with arguments a,b,c if 𝑓 𝑥 =
4. Define cubic spline.
5. Write down the expression for and at X=Xn by Newon’s backward difference formula.
6.Taking h=0.5,evaluate using Trapezoidal rule.
8. State the Milen’s predictor and corrector formulae.
9. Obtain the finite difference scheme for the differential equation 2y’’(x)+y(x)=5.
10. State whether the Crank Nichollson’s scheme is an explicit or implicit scheme.Justify.

PART-B(5*16=80)

11.a.1)Find the numerically largest eigen value of A=
25 1 2
1 3 0
2 0 −4
And its corresponding eigen vector by power method taking the initial eigen vector as (1 0 0 )T (upto three decimal places). (8)
2)Using Gauss Jordon method find the inverse of
2 2 6
2 6 −6
4 −8 8. (8)
Or
b)1. Solve the system of equations by Gauss Jordon method :
5𝑥1 − 𝑥2 = 9; −𝑥1 + 5𝑥2 − 𝑥3 = 4; −𝑥2 + 5𝑥3 = −6 (8)
2)Using Gauss –Seidel method solve the following system of linear equations
4x+2y+z=14;x+5y-z=10;x+y+8z=20. (8)
12)a)1)find f(3)by Newton’s divedend difference formula for the following data
X: -4 - 1 0 2 5
Y:1245 33 5 9 1335 (8)
2) Using Lagrange ‘s interpolation formula find y(2) from the following data:
Y(0)=0; Y(1)=1;Y(3)=81;Y(4)=256;Y(5)=625. (8)
Or
b)Fit the cubic spines of the following data:
X: 1 2 3 4 5
Y: 1 0 1 0 1 (16)
13)a) 1) For the given data find the first two derivatives at x=1.1
X: 1.0 1.1 1.2 1.3 1.4 1.5 1.6
Y: 7.989 8.403 8.781 9.129 9.451 9.750 10.031 (8)