Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 4th Sem New 2140105 Numerical Methods Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2140105 Date: 07/12/2019
Subject Name: Numerical Methods
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) State the numerical methods for solving initial value differential
equations.
03
(b)
Implement bisection method to solve 0 9 4
3
? ? ? x x
04
(c) Describe the fitting of a straight line y=ae
bx
and fit it for the data,
x 2.30 3.10 4.00 4.92 5.91 7.20
y 33.0 39.1 50.3 67.2 85.6 125.0
07
Q.2 (a) State the formulae for Lagranges interpolation methods. 03
(b) Using the Lagranges formula find the polynomial and evaluate f(9).
x 5 7 11 13 17
y 150 392 1452 2366 5202
04
(c) Obtain cubic spline for every subinterval from the following data:
x 0 1 2 3
y 2 -6 -8 2
07
OR
(c) Use Stirling?s formulae for finding y(12.2) from the data:
X 10 11 12 13 14
y 23967 28060 31788 35209 38368
07
Q.3 (a) Use Gauss elimination solve x+4y-z=-5, x+y-6z=-12, 3x-y-z=4. 03
(b)
Use Trapezoidal rule to evaluate
?
?
6
0
2
1
1
dx
x
taking h=1, step length.
04
(c) Describe the Newton Raphson method in brief and evaluate
N for N=10.
07
OR
Q.3 (a) Use Gauss Jordan method to solve 3x+y+2z=3, 2x-3y-z=-3, x+2y+z=4. 03
(b) Use Simpsons 3/8 rule to evaluate, taking h=0.2 and n=6 for
?
? ?
4 . 1
2 . 0
) log (sin dx e x x
x
04
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Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2140105 Date: 07/12/2019
Subject Name: Numerical Methods
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) State the numerical methods for solving initial value differential
equations.
03
(b)
Implement bisection method to solve 0 9 4
3
? ? ? x x
04
(c) Describe the fitting of a straight line y=ae
bx
and fit it for the data,
x 2.30 3.10 4.00 4.92 5.91 7.20
y 33.0 39.1 50.3 67.2 85.6 125.0
07
Q.2 (a) State the formulae for Lagranges interpolation methods. 03
(b) Using the Lagranges formula find the polynomial and evaluate f(9).
x 5 7 11 13 17
y 150 392 1452 2366 5202
04
(c) Obtain cubic spline for every subinterval from the following data:
x 0 1 2 3
y 2 -6 -8 2
07
OR
(c) Use Stirling?s formulae for finding y(12.2) from the data:
X 10 11 12 13 14
y 23967 28060 31788 35209 38368
07
Q.3 (a) Use Gauss elimination solve x+4y-z=-5, x+y-6z=-12, 3x-y-z=4. 03
(b)
Use Trapezoidal rule to evaluate
?
?
6
0
2
1
1
dx
x
taking h=1, step length.
04
(c) Describe the Newton Raphson method in brief and evaluate
N for N=10.
07
OR
Q.3 (a) Use Gauss Jordan method to solve 3x+y+2z=3, 2x-3y-z=-3, x+2y+z=4. 03
(b) Use Simpsons 3/8 rule to evaluate, taking h=0.2 and n=6 for
?
? ?
4 . 1
2 . 0
) log (sin dx e x x
x
04
2
(c)
Describe method of False position and solve
x
xe x ? cos within the
interval (0,1).
07
Q.4 (a) State the finite difference method for laplace equation 03
(b)
Solve heat equation
22
22
0
uu
xt
??
??
??
over a rectangular slab that is 20 cm
wide and 10 cm high All edges are kept at
0
0 except the right edge which
is maintained at
0
100 . There is no heat gain or lost from the surface of
the slab. Place nodes with step length of 5 cm to generate grids and solve
using finite difference method.
04
(c) State the Taylors method and solve equation,
00
0, 1.
dy
x y with x y
dx
? ? ? ? Let h=0.1 and find four iterations.
07
OR
Q.4 (a) State the finite difference quotients for first and second order
derivatives.
03
(b) Solve y?+4y+1=0 with y(0)=0, y(1)=0, Using h=0.5 implement finite
difference approach.
04
(c) State the Picard?s formula and solve the equation for x=0.1
x y
x y
dx
dy
?
?
?
with y(0)=1.
07
Q.5 (a) Discuss in brief finite difference and finite element approach 03
(b) Describe the Galerikin method in brief. 04
(c)
Solve using Runge Kutta 4
th
order method
2 2
2 2
x y
x y
dx
dy
?
?
?
y(0)=1 for x=0.2,x=0.4.
07
OR
Q.5 (a) Discuss the shooting approach for boundary value problems. 03
(b) Solve u?=u, u?(1)=1.1752, u?(3)=10.01787 using appropriate method. 04
(c)
Implement shooting method to solve " (1 )
5
x
u u x ? ? ? with u(1)=2,
u(3)=-1.
07
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This post was last modified on 20 February 2020