My Profile
Active Members
TodayLast 7 Days
more...
Awards & Gifts
Online Exams
Fresher Jobs
Our fresher job section is exclusively for fresh graduates! Find jobs for freshers in major Indian
cities including Bangalore, Chennai, Hyderabad, Pune or Kochi
Resources
Find educational articles, blogs, discussion threads and other resources.
Colleges
Find details about any college in India or search for courses.
|
Download Model question papers & previous years question papers
|
Posted Date: 23 Aug 2009 Posted By: R, MURALI Member Level: Bronze
|
2009 Tamil Nadu State B.E Electrical and Electronics ANNA UNIVERSITY - IV SEMESTER EXAMS Question paper
ANNA UNIVERSITY- COMBATORE
B.E./ B.TECH. DEGREE EXAMINATION - JUNE 2009.
ELECTRICAL & ELECTONICS ENGG. - FOURTH SEMESTER
NUMERICAL METHODS
PART-A
Answer all questions. (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 following 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 find 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 3 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 four 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. Find y(0.1) by Euler’s method.
15. State fourth order Runge-kutta formula.
16. Write the Adam’s Predictor and Corrector formula.
17. Write the diagonal five point formula for solving Laplace equation.
18. Name the two methods that you can use to solve one dimensional heat equation.
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 one dimensional heat equation for ?=1/2.
PART-B
Answer any five. (5*12=60)
21. a) Find the root of the equation 3x+sinx=ex by Newton’s method. (6) b) Solve the following equations x+2y+z=3, 2x+3y+3=10, 3x-y+2z=13 using Gauss Jordan method (6)
22. a) Using cubic spline, find y(0.5) given M0=M2=0 and the table (6)
X 0 1 2
Y -5 -4 3
b) From the following table, find 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 given below . Find 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 modified Euler’s method find y(0.2), y(0.4), given y’=y+ex , y(0)=0. (6)
b) Using Milne’s method find y(0.4) given 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 given u(0,t)=0, u(4,t)=0, u(x.0)=x(4-x) and assuming h=1 find the values of u upto t=5 by Schmidt method. (6)
b) Solve y’’-xy=0 given y(0)=-1, y(1)=2 by finite difference method taking h=1/3.
26. a) Find the root of the equation x4-x-10=0 by iteration method. (6)
b) Using Lagrange’s formula for the interpolation find the values of f(4) from the following table.
(6)
X 0 2 3 6
f(x) -4 2 14 158
27. a) Find the interpolating polynomial for y from the following data using Newton’s forward formula
(6)
X 4 6 8 10
Y 1 3 8 16
b) Solve Uxx+Uyy=0 for the following square mesh with boundary conditions as shown below. (6) A 1 2 B
1 U1 U2 2
2 U3 U4 1
D 2 1 C
28. a) Evaluate ?512 dx/x using Gaussian quadrature three point formula. (6)
b) Solve the following system of equations
20x+y=2z=17, 3x+20y-z=-18, 2x-3y+20z=25, by using Gauss Jacobi method. (6)
Return to question paper search
|
|
|
Submit Previous Years University Question Papers and make money from adsense revenue sharing program
Are you preparing for a university examination? Download model question papers
and practise before you write the exam.
|
Advertise Here
|