Numerical Methods MA2264 MJ2014 6th Semester Question Paper

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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 ๐‘“ ๐‘ฅ =
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.
7.State the advantages and disadvantages of the taylors series method.
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 :
5๐‘ฅ1 − ๐‘ฅ2 = 9; −๐‘ฅ1 + 5๐‘ฅ2 − ๐‘ฅ3 = 4; −๐‘ฅ2 + 5๐‘ฅ3 = −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)

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