M.Sc. DEGREE EXAMINATION, APRIL 2016.
Physics
ELEMENTARY NUMERICAL ANALYSIS
(2011 onwards)
Time 3 Hours Maximum 75 Marks
Part A (10 2 20)
Answer all questions.
All questions carry equal marks.
1. What is called round off error? Give an example.
2. What are the demerits of bisection method?
3. What is called linear interpolation?
4. For a set of four data, what is the maximum order of
divided differences needed for interpolation?
5. What are the uses of forward interpolation and backward
interpolation formulas?
6. Write the algorithm of trapezoidal rule.
7. What is the truncation error of Simpson's one-third rule?
8. Write down the algorithm of Euler's method for the
solution of first-order ODE.
Sub. Code
521501
RW-10944
2
Ws9
9. What is called a singular matrix?
10. What is called partial pivoting?
Part B 5 25)
Answer all questions.
All questions carry equal marks.
11. Explain the procedure of least-squares fitting of a
data set with an exponential function.
Or
Estimate the order of convergence in Newton-
Raphson method.
12. Discuss the computational procedure of non-linear
interpolation.
Or
Deduce Newton's forward interpolation formula.
13. Evaluate the integral between the
limits by using the trapezoidal rule with a
step interval of h
Or
Derive Simpson's one-third rule.
14. Discuss Taylor's series method of solving first-order
ODE and write down the corresponding algorithm.
Or
Find the solution at x 0.2 of the differential
equation 2xy given that 0 by
taking the step interval h 0.1.
RW-10944
3
Ws9
15. Discuss the computational procedure of Gaussian
elimination to solve a system of linear equations.
Or
Discuss the LU-factorization procedure of solving
simultaneous equations.
Part C 10 30)
Answer any three questions.
All questions carry equal marks.
16. Compute the root of x3 9x 0 that lies between
2 and 4 by using secant method.
17. From the following data set, find the value of y at x 84.
x 40 50 60 70 80 90
y 184 204 226 250 276 304
18. Estimate the value of 3
1 loge 2 by
evaluating x3 dx between the limits
using Simpson's one-third rule with a step size of
h 0.25.
19. Applying RK-4 method, obtain the values of at
x 0.1 and 0.2, for the differential equation
given that . Take h 0.1.
20. Solve by Gauss-Siedel method
8x 3y 2z 20, 4x z 33 and 6x 3y 35.