Anna University Chennai 2009-5th Sem B.E Electrical and Electronics Engineering ANNA UNIVERSITY - IESTER S - university paper

ANNA UNIVERSITY- COMBATORE
B.E./ B.TECH. DEGREE exam - JUNE 2009.
ELECTRICAL & ELECTONICS ENGG. - 4th SEMESTER
NUMERICAL METHODS
PART-A
ans all ques.. (20*2=40)
1. What is the condition for the convergence of the iteration method.
2. To which forms are the augmental matrices transform in the Gauss Jordan and Gauss Elimination method.
3. Solve the subsequent system 2x+y=3, 7x-3y=4 by Gauss elimination method.
4. Write down the iterative formula for vN in Newton’s method.
5. Which methods are used for finding the polynomial if the intervals are unequal.
6. If f(x)=1/x obtain the divided difference f(a,b).
7. State Lagrange’s interpolation formula.
8. Write the Newton’s forward interpolation formula for equal intervals.
9. Write the Gaussian quardrature three point formula.
10. What are the orders of the errors in Trapezoidal and Simpson’s rules of numerical integration.
11. State Simpson’s 3/8th rule formula.
12. Evaluate ?01e-x2dx by dividing the range of integration into 4 equal parts using Simpson’s 1/3rd rule.
13. State Taylor series method formula.
14. Given dy/dx=(y-x)/(y+x) with y=1 for x=0. obtain y(0.1) by Euler’s method.
15. State 4th order Runge-kutta formula.
16. Write the Adam’s Predictor and Corrector formula.
17. Write the diagonal 5 point formula for solving Laplace formula.
18. Name the 2 methods that you can use to solve 1 dimensional heat formula.
19. Solve by finite difference method for y’’=y, y(0)=-1, y(2)=15 taking h=1.
20. Write the explicit formula to solve 1 dimensional heat formula for ?=1/2.
PART-B
ans any five. (5*12=60)
21. a) obtain the root of the formula 3x+sinx=ex by Newton’s method. (6) b) Solve the subsequent equations x+2y+z=3, 2x+3y+3=10, 3x-y+2z=13 using Gauss Jordan method (6)
22. a) Using cubic spline, obtain y(0.5) provided M0=M2=0 and the table (6)
X 0 1 2
Y -5 -4 3

b) From the subsequent table, obtain f(6) using Newton’s interpolation formula (6)
X 1 2 7 8
f(x) 1 5 5 4


23. a) The population of certain town is provided beneath . obtain the rate of growth of the population in 1971. (6)
Year:x 1931 1941 1951 1961 1971
Population in thousands 40.62 60.80 79.95 103.56 132.65

b) Evaluate ?p0 sinx dx by dividing the range into ten equal parts using Trapeziodal rule. (6)
24. a) Using replaced Euler’s method obtain y(0.2), y(0.4), provided y’=y+ex , y(0)=0. (6)
b) Using Milne’s method obtain y(0.4) provided dy/dx=xy+y2, y(0)=1, y(0.1)=1.1167, y(0.2)=1.2767, y(0.3)=1.5023. (6)
25. a) ?2u/?x2-2?u/?t=0 provided u(0,t)=0, u(4,t)=0, u(x.0)=x(4-x) and assuming h=1 obtain the values of u upto t=5 by Schmidt method. (6)
b) Solve y’’-xy=0 provided y(0)=-1, y(1)=2 by finite difference method taking h=1/3.
26. a) obtain the root of the formula x4-x-10=0 by iteration method. (6)
b) Using Lagrange’s formula for the interpolation obtain the values of f(4) from the subsequent table.
(6)

X 0 2 3 6
f(x) -4 2 14 158


27. a) obtain the interpolating polynomial for y from the subsequent data using Newton’s forward formula
(6)
X 4 6 8 10
Y 1 3 8 16


b) Solve Uxx+Uyy=0 for the subsequent square mesh with boundary conditions as shown beneath. (6) A one two B
1 U1 U2 2
2 U3 U4 1

D two one C
28. a) Evaluate ?512 dx/x using Gaussian quadrature 3 point formula. (6)
b) Solve the subsequent system of equations
20x+y=2z=17, 3x+20y-z=-18, 2x-3y+20z=25, by using Gauss Jacobi method. (6)

Earning:   Approval pending.