Numerical Analysis 2017 – BSc Computer Science Part 2 (MJPRU)

Paper code: 13512
1512
B.Sc. (Computer Science) (Part 2)
Examination, 2017
Paper No. 1.3
NUMERICAL ANALYSIS

Time: Three Hours] [Maximum Marks: 50

 

Note: Attempt five questions. All questions carry equal marks.

1. (a) Use Lagrange’s formula to find f(6) from the following table:

(b) The population (in thousands) of a town in the year 1931, …………, 1971 are as ahead:

Find the population of the town in 1946 by applying Gauss’s backward formula.

2. (a) Use the Milne’s method to solve the equation  with y(0)=0 from x=0 to x=1.

(b) Use the Runge-Kutta method to approximate y when x=0.1 given that x=0 when y=2 and \frac{dy}{dx}=y-x.

3. (a) Find a real root of the equation  using the Newton-Raphson method.

(b) Find the cube root of 10 correct to three decimal places by Regula-Falsi method.

4. (a) Evaluate  by Simpson’s one-third rule by dividing the interval into 6 parts.

(b) Evaluate  by Trapezoidal rule.

5. (a) Solve the following equations by Gauss Elimination method:

(b) Solve by Jacobi iteration method the system of equations:

6. (a) State and prove Newton’s-Gregory formula for backward interpolation.

(b) Apply Newton’s dividend difference formula to find the value of f(8) if f91)=3, f(3)=31, f(6)=223, f(10)=1011, f(11)=1343.

7. (a) Find the function  in powers of x-1 given that

, , , .

(b) Write short notes on the following:

1. Relative Error and Absolute Error
2. Percentage Error and Round Off Error

8. (a) Solve the system linear of equations by the Gauss-Seidel method (4 iterations):

(b) Solve the following:

(i) Prove that:

(ii) Prove that:

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