WBUT Question Papers Numerical Methods EC B Tech Sem Third 20112012
WBUT Question Papers
Numerical Methods EC B Tech Sem Third 20112012
Time Allotted : 3 Hours
^{Marks} ‘■ ^{70}
7Tie figures in the margin indicate full marks.
Candidates are required to give their answers in their own words
as far as practicable.
GROUP – A ( Multiple Choice Type Questions )
 Choose the correct alternatives for any ten of the following .
10 x 1 = 10
i) Which of the following is not a computational error ?
■ ‘ f ‘ ■ a) Truncation error b) Roundoff error
c) Inherent error d) None of these.
ii) NewtonRaphson method fails when
a) /'(*)= 1 ^{b}) /’ ( x) = 0
_{c)} f ( _{x} ) = – 1 d) /” ( x ) = 0.
CS/B.TECH(BME(N)/ECE(N)/EE(N)/EEE(N)/EIE(N)/ICE(N)/PWE(N))/ SEM3/M(CS)301 /201112 ‘
ili) Finite difference method is used to solve
a) a system of linear simultaneous equations
b) a system of nonlinear simultaneous equations
c) partial differential equations
d) nonlinear equations.
iv) Regulafalsi method has a convergence rate of the order of
^{a}) 2 b) 162
c) 1 d) none of these.
v) GaussSeidel method for solution of a system of linear simultaneous equations converges if
n
^{a}> I “,( I ^{S} X I Oy 
j = l j* i
«. n
^{b}> I ^{a} ,i I > X I a ,J I
i ^{J}‘,’
^{f} J*i .
^{c) }I ^{a},i I / I I = i
d) none of these.
vi) Modified Euler’s method has a truncation error of the order of
a) h b) h^{2}
c) h^{A} d) h^{3}.
3003 (N)
CS/B.TECH(BME(N)/ECE(N)/EE(N)/EEE(N)/EIE(N)/ICE(N)/PWE(N))/
SEM3/M(CS)301 /2011 12
vii) Divided difference interpolation formula can be used for
a) the tabular values with independent variable unequally spaced
b) inverse interpolation
c) both (a) and (b)
d) none of these. .
viii) Truncation error in Simpson’s ^ ^{rc}* ^{m}^^{e} *^{s} £^{iven} by
^{a) }^{h4}^{/}“’^{U)}^{a}–^{i}‘^{b} . ^{b) }^{hS} ‘ ^{a}^^{b}
c) h^{4} /'”U) • ci<^<b
^{d) }^ n^{4}
ix) Which of the following relations is true ?
a) E – 1 – A, A – V = A V
b) E = 1 – A, A + V = A V
;
Cl E = 1 + A, iA + V = A V
f *
d) E = 1+A, AV=AV.
x) Trapezoidal method can be used to integrate numerically a function represented in tabular form
a) with odd number of intervals only
b) with even number of intervals only
c) both (a) and (b)
d) none of these.
CS/B.TECH(BME(N]/EGE(N)/EE(N)/EEE(N)/EIE(N)/ICE{N]/PWE(N))/ SEM3/M(CS)~301/201112
xl) Condition of convergence for Euler’s method 0> I 1 + kf'(x_{t}. y_{t})  < 1
b)  1 + hf'[x_{t}, y_{(})  < 1 0 1 + y _{(})  > 1 .
d) I 1 + hf'[x_{r} y .)  > 1.
xii) Milne’s corrector formula is
h ^{1}
a) =y_{n} ^{+} 3(yl, +4y^ _{+} 4y’_{<+1})
y_{nf}i =y_{n}i ^{+} §(y’_{n}, + 4y^{l}_{n} + *y^{l}_{n + }_{1})
i 4h / i i . i ■*
U _{n} + i =yn^{+} 3″(yni ^{+4}yn^{+}4y_{n+1})
d) none of these.
GROUP B
( Short Answer Type Questions )
% . ^{1} ■ ‘ ‘ . ’ *
Answer any three of the following. 3×5= 15
 Given t#e function y = ^ , show that the divided difference of n^{th} order
y[x_{Q}, X_{x}, X_{2}, … , ^_{n}] = (“l)^{n}/(x_{0}x_{1}x_{2}…x_{r[})
 Solve the following system of linear equations by Gauss Seidel iterative method :
9x + 2y + 3z = – 7 , ■ * x ~ 6y + 2z = – 2
CS/B.TECH(BME(N)/ECE(N)/EE(N)/EEE(N)/EIE(N)/ICE(N]/PWE(N))/ SEM3/M(CvS)301 /2011 12 4. Fit a polynomial to the following table of values using Lagrange interpolation formula :

Find the value of y when 
a) x = 2
b) x = 35.
 Find the value of using NewtonRaphson method. Result
t
is required to be corrected up to 4 decimal places.
 Solve the following equation using bisection method :
 3x + sin x – e ^{[1]} = 0 Take x_{Q} = 1 and a: _{]} = 0.
Result is required to be corrected up to 2 decimal places.
GROUP C ( Long Answer Type Questions )
Answer any three of the following. 3 x 15 = 45
 a) Derive the orde^r of convergence for NewtonRaphson
 method. 5
b) Solve the following initial value problem using Euler’s method :
^ = x^{2} + y with y ( 0 ) = 1.
Compute the first 5 steps of the solution with h = 01.
Compare the results ( % relative error ) with those obtained from the exact solution
y = 3e^{x} – x^{2} – 2x – 2. 10
 a) Prove by the method of Induction :
^{&m} y _{r} =^{vm}y_{r+}
m
b) Use Newton’s formula to find the area of a circle of diameter 98 cm. ‘ 5
c) Derive Lagrange interpolation formula. , 5 
Derive the expression for total truncation error associated with Simpson’s ^ rd method. 8
Evaluate the following integral using trapezoidal method :
2
I = J (l/(*^{2} + 4)Jdx
Take h = 0125. Hence obtain the value of n. 7
10. a) Solve the following system of equations using LU factorization method. 8
3x – y + 2z = 12
x + 2y + 3z = 11
2x – 2y – z = 2.
b) Find the inverse of the following matrix : 7
84 0
– 4 84 L 0 – 4 8
5
b) Derive Newton’s Backward difference interpolation formula. 5
c) Derive 4th order RungeKutta formula for solution of initial value problem of ordinary differential equation. 5
Recent Comments