University of Sargedha BS 5* Term Examination 2018 Subicct: Computer Science Paper: Numerical Computing (CS: 3941) Time Allowed: 2:30 Hour

University of Sargedha

BS 5* Term Examination 2018

Subicct: Computer Science Paper: Numerical Computing (CS: 3941)

Time Allowed: 2:30 Hour

Maximum Marks: 80

Objective Part

(Compulsory)

Q. No. I Strite short answers of the following quertione each in 2-3 lines only on the anewer book

having 2 marks each.

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-(i) Define absolute and relative error.

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(a) What in the convergence condistes for fixed-point Iteration.

- (1) Explain round off error with example.

-(iv) Graphical representation of bisection method.

- (v) Explain pivoting In system of linear equations.

-

(vi) Write steps of power method for eigen values.

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- (vil) Write divided difference formula for interpolation.

-(vill) Write any formula of numerical differentiation.

•(ix) Write composite formula for trapezoidal rule.

- (x) Write formula for Gaussian Quadrature Formulne.

-(xi) What is Zeros of polynomial.

• (xil) Define transcendental and algebraic equation.

- (xili) What is numerical stability criteria to solve differential equations?

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(xiv) Draw table for divided difference of the following data (0, 1), (1,

1) and (2, 2).

- (x) Define is interpolation.

-(xvi) Define is extrapolation.

(Subjective Part)

Note: Attempt any three questions.

Q. No. 2: Consider the function f(=) = cos(s) - z =

0. Approximate the root of / using New-

tons method starting from

(16)

Q. No. 3: Construct the Langrange interpolating polynomial for the function f(=) = cos(2) + sin(2),

where to = 0, =, = 0.25, =z = 0.5, =g = 1.0.

(16)

Q. No.

4C Using composite Simpson's rule to approximate the following integral with partition

tan(z) dz

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(16)

Q. No. 5: Use the Rang-Kutta method of order four with ^ = 0.2, N = 10 and i, = 0.2i to ob-

tain approximation to the solution of initial value problem y'= y-p+ 4,051 ≤ 2, (0) = 0.5. (16)

Q. No. 6: Use Gauss Seidel Iteration technique to find approximate solution of

102g - =a + 2zg = 6,

-=, + +11z, - 3y + 32, = 25,

2=1 - 52 + 10zy -24=-11,

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