North Maharashtra University 2008 B.Sc Mathematics S.YBSc - MTH – 222 (B) (Numerical Analysis) - Question Paper

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NORTH MAHARASHTRA UNIVERSITY, JALGAON

Class : S.Y. B. Sc. Subject : Mathematics
Paper : MTH – 222 (B) (Numerical Analysis)

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1 : ques. of two marks
1) State the Taylor’s series for y(x) at x =x0 if y(x) is the exact solution of y'
= f(x,y) with y(x0) = y0.
2) State the Euler’s general formula for y' = f(x,y) with y(x0) = y0.
3) What is the difference ranging from Euler’s method and Euler’s replaced
method.
x 0 0.5 one 1.5 two 2.5
y 0.1 0.45 2.15 9.5 40.35 180.75
x 2.2 2.7 3.5 4.1
y 65 60 53 50
x one two three four five 6
y 1.5 4.6 13.9 40.1 125.1 299.5
x one two three four five 6
y 15.3 20.5 27.4 36.6 49.1 65.6
x one two three four five six seven 8
y 15.3 20.5 27.4 36.6 49.1 65.6 87.8 117.6
x(Temperature) 77 100 185 239 285
y(Solubility) 2.4 3.4 seven 11.1 19.6
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4) State the Runge-Kutta 2nd order formulae.
5) State the Runge-Kutta 4th order formulae.
6) Which method is more useful in solving the differential formula y' =
f(x,y) with y(x0) = y0?
7) State the iteration formula for Euler’s replaced method, where y' = f(x,y)
with y(x0) = y0.
8) provided that
dx
dy = y – x with y(0) = 2. obtain K1 and K2 .
9) provided that
dx
dy = xy1/3 with y(1 = one obtain K1 and K2 .
10) provided that
dx
dy =
y x
y x
+
- with y(0) = one and h = 0.1 obtain y(0.1) by Eulers
method.
11) provided y' = x2 + y with y(0) = one and 0.1. obtain y(0.1) by Euler’s replaced
method.
12) provided y' = x + y with y(0) = one and 0.2. obtain y(0.2) by Euler’s
replaced method.
13) provided y' = y2 – x2 with h = 0.1and y(0) = 1, obtain y(0.1).
14) obtain K1 and K2 by Runge-Kutta forth order formulae where y' = 3x +
2
y
with y(0.1) = one and h = 0.1.
15) obtain y(x) if y' = x + y, with y(0) = 1, x ? [0 , 1] by Taylor’s series
expansion.
16) provided that y' =
y x
y x
+
- with y(0) = one and h = 0.025 calculate y(0.05) using
Euler’s method.
17) provided that y' = –2y with y(0) = one and h = 0.1, calculate y(0.2) using
Euler’s method.
18) Determine the value y(0.05) by Euler’s replaced method, provided that y' =
y + x2 with y(0) = one and h = 0.05.
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19) Determine the value y(0.01) using Euler’s replaced method, provided that y'
– y – x2 = 0 with y(0) = one and h = 0.01.
20) provided that
dx
dy = x + y with y(0) = one and h = 0.1, calculate y(0.1) by

Earning:   Approval pending.