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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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