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PROGRAM:
BCA (REVISED 2007)
SEMESTER:
3RD SEM
SUBJECT
CODE & NAME: DESIGN: BC0043-COMPUTER
ORIENTED NUMERICAL METHODS
CREDIT:
4
BK
ID: B0804
MAX.
MARKS: 60
Q.1:
Find a real root of 2x – log10 x = 7 correct to 3 decimal places using
iteration method.
ANS:
Let
f (x) = 2x – log10 x – 7. Now
Q.2:
(i) Unique
solution
(ii)
Infinite number of solutions
(iii) No
solution.
ANS:
3x1 + 20x2
–x3 = –18
2x1 – 3x2 +
20x3 = 25
20x1 + x2 –
2x3 = 17
ANS:
Q.4:
(i)Fit a parabola of second degree y = a + bx + cx2 for the data:
(ii) Use
Lagrange’s interpolation formula to fit a polynomial for the data :
Hence
estimate y at x = 2
ANS:
(i)
The normal equations for y = a + bx + cx2 are
Q.5:
Given dx/dy = 1 + xy, y(0) = 2. Find
y(0.1), y(0.2) and y(0.3) by modified Euler’s method.
ANS:
Here
x0 = 0, y0 = y(0) = 2 and f(x, y) = 1 + xy
Q.6:
Solve y’+ (1 + x) y’ – y = 0, with y(0) = y’(0), y(1) + y’(1) = 1, h = 0.5.
ANS:
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