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

Runge-Kutta 4th order formulae.
21) Using Runge-Kutta 4th order formulae, calculate y(0.2), provided that y'
+ y2 = x with y(0) = one and h = 0.2.
22) calculate y(0.1) by Runge-Kutta 2nd order formulae, provided that y' =
y – x with y(0) = two and h = 0.1.
2 : Fill in the blanks/ Multiple option ques. of 1
marks
1) If the exact solution of formula y' = f(x,y) with y(x0) = y0 then
Taylor’s series expansion for y(x) about the point x = x0 is y(x) = - - - -
a) y0 + xy0' + x2 y0'' + - - - b) y0 + h2y0' + h2y0'' + h3y0''' + - - -
c) y0 + hy0' + h(y0'')2 + - - - d) none of these
2) There is a class of methods as - - - - which do not require the
computations of higher order derivatives and provide greater accuracy.
a) Euler’s method b) Euler’s replaced method
c) kutta d) Runge-Kutta of 2nd order
3) Runge-Kutta method of 2nd order is the - - - - method
a) Euler’s method b) Taylor’s method
c) Euler’s replaced d) none of these
4) For y' = y + x with y(0) = one and h = 0.1 the value of K1 in Runge-Kutta
fourth order method is - - - -
a) 0.1 b) 1.0 c) 0.01 d) 0.11
22
5) In Runge-Kutta 4th order method K4 = - - - -
a) hf(x1 + h , y1 + K3) b) hf(x1 + h , y1 + K2)
c) hf(x1 + h , y1 + K1) d) f(x1 + h , y1 + K3)
6) In Runge-Kutta 2nd order method K2 = - - - -
a) f(x0 + h , y0 + K) b) f(x0 + h , y0 + K1)
c) hf(x0 + h , y0 + K1) d) hf(x0 + h , y0 + K2)
7) In Euler’s method , yn+1 = - - - -
a) yn b) yn + f(xn , yn)
c) yn + hf(xn , yn) d) none of these
8) The iteration formula for Euler’s replaced method is y1
n+1 = y0 + - - - -
a) f(x0 , y0) + h b)
2
h [ f(x0 , y0) + f(x1 , y1)]
c)
2
h [ f(x0 , y0) + f(x1 , y1
(n))] d) none of these
9) Taylor’s series method is the - - - -
a) boundary value issue b) initial value issue
c) valued issue d) none of these
10) The value of y1(0) i.e. y(0.05) is - - - -when y' = x2 + y with y(0) =- 1
and h = 0.05.
a) 1.5 b) 1.05 c) 1.052 d) 1.0525
3 : ques. of six marks
1) discuss the method of finding the solution of the differential formula y' =
f(x,y) with initial condition y(x0) = y0 by Taylor’s series method.

Earning:   Approval pending.