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Code No: D109112001 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

M.Tech I Semester Regular Examinations March 2010 COMPUTER ORIENTED NUMERICAL METHODS

(STRUCTURAL ENGINEERING) Time: 3hours Max.Marks:60

Answer any five questions All questions carry equal marks

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1(a) What is an Augmented Matrix? Explain how does Linear System of Equations be represented as Augmented Matrix. (b) Solve the following system of equations using Gauss-Elimination Method

=

2.(a) Explain the Givens method for Symmetric matrices. (b) Use the House Holder’s Transformation to reduce the matrix

A =

3(a) Define Interpolation. Explain its advantages and disadvantages. (b) Find the unique polynomial P(x) of degree 2 or less such that P(1)=1, P(3)=27, P(4)=64 using Lagrange’s Interpolation 4. Obtain Cubic Spline approximation for the function defined by the data

X 0 1 2 3 F(x) 1 2 33 244

5. Prove that one can use repeated Richardson’s extrapolation for the formula

(x) = , what are the coefficients in extrapolation scheme.

6. Evaluate the integral I= using the Trapezodial Rule with

h=k=0.5 7. Explain Newton-Cotes integration method for Numerical Integration. 8. Solve the initial value problem = , U(0)=1 with h=0.2 on the interval [0,0.4] using backward Euler method.

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