Download GTU BE/B.Tech 2019 Winter 3rd Sem New 3130107 Partial Differential Equations And Numerical Methods Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 3rd Sem New 3130107 Partial Differential Equations And Numerical Methods Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? III (New) EXAMINATION ? WINTER 2019
Subject Code: 3130107 Date: 26/11/2019

Subject Name: Partial Differential Equations and Numerical Methods
Time: 02:30 PM TO 05:00 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) Discuss in brief least square method for straight line 03
(b) Fit a straight line to
x 1 2 3 4 5
y 14 27 40 55 68

04
(c) State the method of false position and solve
3
2 5 0 xx ? ? ?


07

Q.2 (a) Apply Newton Raphson to solve
0
sin cos 0, 3.1416 x x x x ? ? ?
03
(b) Solve using Gauss elimination method
5 2 3 18
7 3 22
2 6 22
x y z
x y z
x y z
? ? ?
? ? ? ?
? ? ?

04
(c) Find the value of y when x=390 using Newtons formula
from the table
x 100 150 200 250 300 350 400
y 10.63 13.03 15.04 16.81 18.42 19.9 21.47

07
OR
(c) Use Lagranges formula to obtain y for x=2 using,
x 0 1 3 4
y -12 0 6 12

07
Q.3 (a) Apply Trapezoidal rule to evaluate
5
10
1
log xdx
?
with h=0.5.
03
(b) State the formula for Secant method 04
(c) Apply Runge kutta 4
th
order method to solve
2
, (0) 1.
dy x
yy
dx y
? ? ? Compute value for y(0.4) and
y(0.5).
07
OR


Q.3 (a) Apply the Simpson 3/8 rule
1
0
1
1
dx
x ?
?
with h=0.25
03
(b) State the formula for Cubic spline interpolation


04
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? III (New) EXAMINATION ? WINTER 2019
Subject Code: 3130107 Date: 26/11/2019

Subject Name: Partial Differential Equations and Numerical Methods
Time: 02:30 PM TO 05:00 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) Discuss in brief least square method for straight line 03
(b) Fit a straight line to
x 1 2 3 4 5
y 14 27 40 55 68

04
(c) State the method of false position and solve
3
2 5 0 xx ? ? ?


07

Q.2 (a) Apply Newton Raphson to solve
0
sin cos 0, 3.1416 x x x x ? ? ?
03
(b) Solve using Gauss elimination method
5 2 3 18
7 3 22
2 6 22
x y z
x y z
x y z
? ? ?
? ? ? ?
? ? ?

04
(c) Find the value of y when x=390 using Newtons formula
from the table
x 100 150 200 250 300 350 400
y 10.63 13.03 15.04 16.81 18.42 19.9 21.47

07
OR
(c) Use Lagranges formula to obtain y for x=2 using,
x 0 1 3 4
y -12 0 6 12

07
Q.3 (a) Apply Trapezoidal rule to evaluate
5
10
1
log xdx
?
with h=0.5.
03
(b) State the formula for Secant method 04
(c) Apply Runge kutta 4
th
order method to solve
2
, (0) 1.
dy x
yy
dx y
? ? ? Compute value for y(0.4) and
y(0.5).
07
OR


Q.3 (a) Apply the Simpson 3/8 rule
1
0
1
1
dx
x ?
?
with h=0.25
03
(b) State the formula for Cubic spline interpolation


04
2


(c) State the Picard ?s method to solve
2
dy
xy
dx
?? subject to condition y=1,x=0.
07
Q.4 (a) State the classification of partial differential equation. 03
(b) Solve pq=k 04
(c)
Solve 1) 2 5 2 0 r s t ? ? ? and 2)
2 2 2 2 2
y p x q x y z ??
07
OR
Q.4 (a) State the parabolic equation with initial conditions 03
(b)
Solve
22
p q m ??
04
(c) Solve one dimensional heat equation
2
2
2
(0, ) 0
( , ) 0 ( ,0) ( )
uu
c with u t
tx
u L t and u x f x
??
??
??
??

07
Q.5 (a) State the Taylors series formula to solve initial value
problem.
03
(b)
Solve
2 2 2
22
2 5 2 0
z z z
x x y y
? ? ?
? ? ?
? ? ? ?

04
(c) State the methods to solve linear partial differential
equations and solve ( ) ( )
zz
mz ny nx lz ly mx
xy
??
? ? ? ? ?
??

07
OR

Q.5 (a) Give the formula for Newton ?s backward interpolation
formula
03
(b) Solve ( ) ( ) ( )(2 2 ) px x y qy x y x y x y z ? ? ? ? ? ? ? 04
(c) Using Lagrange interpolation formula form a polynomial
for,
X 2 2.5 3
y 0.69315 0.91629 1.09861

07

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