LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034B.Sc. DEGREE EXAMINATION – MATHEMATICSSIXTH SEMESTER – APRIL 2012MT 6605 – NUMERICAL METHODS
Date : 20-04-2012 Dept. No. Max. : 100 Marks Time : 1:00 – 4:00
PART – A Answer ALL questions: (10 X 2 = 20 marks)
1. Explain Cramer’s rule.2. Distinguish between Gauss Elimination and Gauss Seidel methods.3. State the condition for convergence in Newton Raphson method.4. What do you mean by transcendental equation?5. Write Newton forward interpolation formula.6. Write any two properties of divided differences.7. Write Stirling’s formula using central difference notation.8. Write the derivatives using Newton’s forward difference formula.9. Define numerical integration.10. Write Simpson’s 1/3rd and 3/8th rule.
PART – B
Answer any FIVE questions: (5 X 8 = 40 marks)
11. Solve by Gauss elimination method: 12. Find the real root of correct to three significant figures using Regula falsi method.13. Write a C program to interpolate using Newton’s forward interpolation formula.14. Use Lagrange’s formula to find the value of y at x = 6 from the following data: x = 3, 7, 9, 10 and the corresponding value of y = 168, 120, 72, 63.15. Using the following data, find f’(5) by Newton’s divided difference formula: : 0 2 3 4 7 9 : 4 26 58 112 466 92216. Derive Laplace Everett’s formula.17. Apply Simpson’s rule to evaluate to two decimal places by dividing the range into 4 equal parts.18. Solve with the initial condition x = 0, y = 0 using Euler’s modified formula.
PART – C
Answer any TWO questions: (2 X 20 = 40 marks)
19. (a) Solve by Gauss Seidel method:
(b) Find by Newton’s method the root of the equation , which is approximately 2, correct to three places of decimals.
20. (a) Given : 0 1 2 5 : 2 3 12 14 find the cubic function of x using Newton’s divided difference formula.
(b) Using Newton’s formula find the value of f(1.5) from the following data: : 0 1 2 3 4 : 858.3 869.6 880.9 892.3 903.6
21. (a) Use Stirling’s formula to find f(1.63) given : 1.50 1.60 1.70 1.80 1.90 : 17.609 20.412 23.045 25.527 27.875 (b)Given X: 0 4 8 12Y: 143 158 177 199 calculate y5 by Bessel’s formula.
22. (a) Apply the fourth order Runge–Kutta method, to find an approximate value of when = 0.2 given that (b) Write a C program to find the value of using Simson’s 1/3 rule.
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