COMPUTER SCIENCE 2MCA-6 : Computational ... - Surana college

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II Semester M.C.A. Degree Examination, June/July 2010
(Y2K5 Scheme)
COMPUTER SCIENCE
2MCA-6 : Computational Numerical Methods
Time : 3 Hours Max. Marks : 80
PAKT _ A
1. Answer any ten fuIl questions. (L0x2=20)
a) Define round off error.
b) Find the real root of the equation x3 - 4x -9 - 0 that lies between? and3 using
bisection method in four stages.
c) Write algorithm for Secant method.
d) Explain Guass Jordan method for a 3 x3 matrix.
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e) Find the Eigen values for the matrix O =
L_ , ? ).
6
1rd
0 Evaluate J
lx'Ox by taking 7 ordinates using Simpson's i Rule.
oJ
g) Using Euler's method solve y' = x2 + xy + y2 with y(0) :1 at x : 0.1 taking
h:0.05.
h) ExplainAitken's t' formula.
r) Write the formula for modified Euler's method.
j) Given x:0 I 2 3
f(x):1 3 7 13
Find the interpolating polynomial that takes the following values using Newton's
backward interpolation formulae.
k) Write the formutra for Lagrange's interpolation formulae.
1) Write the Jacobi's iteration method for a system of 3 equations in 3 unknowns.
P.T.O.

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Answer any two full questions :
PART _ B
(2x15=30)
2. a) Use Newton Raphson method to find ffi
conect to 3 decimal places. 5
b) Find the real root of the equation cos x : 3x - I correct to 3 decimal places using
Regula-falsi method lying between 0 and 1. 5
c) Using Bisection method find the root of the equation x log,o x -1.2
that lies
between 2 and3 car-ry out 5 iterations. 5
3. a) Using Graeffs root squaring method solve the equation x3 -3*- 6x + 8 : 0. 10
b) Find a root of (x) : e" - 3xzby fixed point iteration method. Choose the initial
approximation as zero. 5
4. a) Solve the following system of equations by LU decomposition method
2xr* xz* 4Xr: 12, 4xr* 11x, - x, : 33, 8", - 3xr+ 2xr:20. 8
b) Solve the following equations by relaxation method.
5x-y -z- 3, -X+ 10y -22:7,-x-y+ 102:8. 7
PART - C
Answer any two fulI questions :
5. a) Find the dominant eigen value and the corresponding eigen vector of the matrix
Io-2 zf
n=l-z 3 -rl
^:l- J ' : I using Rayleigh powermethod carry out 5 iterations. 7
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b) UsingNewton's Divided Difference formula find f(2) given
x: 0 | 4 8 10
f(x): -5 -r4 -r25 -21 355 8

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6. a) Forthefollowingdatafind f'(t) and f"(3) g
x: 0 2 4 6 8
f(x): 7 13 43 r4S 367
0.3 I "*
b) Evaluate
Itt-8*')'dx bySimpson's ] Rulebytakingfourordinates. 7
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7 . a) using Runge-Kutta method of fourth order, find y(0.2) given
# = 3x + j with
y (0):1 by taking h:0.1
g
b) Using Picard's method find y(0.1) and y (0.2) given
* = 1+ xy with y (0) :2.