Download GTU B.Tech 2020 Winter 4th Sem 2140105 Numerical Methods Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 4th Sem 2140105 Numerical Methods Previous Question Paper

Seat No.: ________
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?IV (NEW) EXAMINATION ? WINTER 2020
Subject Code: 2140105 Date: 09/02/2021
Subject Name: Numerical Methods
Time: 02:30 PM TO 04:30 PM Total Marks: 56
Instructions:
1. Attempt any FOUR questions out of EIGHT questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.


MARKS
Q.1 (a) Define and name the methods to solve differential
03
equations.

(b) Implement bisection method to solve x3-3x-5=0 upto
04
fourth approximation.

(c) Describe the fitting of
px
y ae for the data,
07
x
0
2
4
y
5.012
10
31.62


Q.2 (a) State the formulae for Newtons backward interpolation
03
methods . Specify the methods used for unequal intervals

(b) Using the Lagrange's formula find the polynomial which
04
fits into the data below:
x
0
1
2
5
y
2
3
12
147

(c) Obtain cubic spline for every subinterval from the
07
following data:
x
0
3
8
y
1
2
3




Q.3 (a) Use Gauss elimination solve x+2y+z=8, 2x+3y+4z=20,
03
4x+3y+2z=16.

(b)
3 1
04
Use Trapezoidal rule to evaluate
dx
taking 4
x
1
subintervals.

(c) Describe the Newton Raphson method in brief and solve
07
x
e 5x




Q.4 (a) Use Gauss Jordan method to solve 10x+y+z=12,
03
x+10y+z=12, x+y+10z=12.

(b)
6
1
04
Use Simpsons 3/8 rule to evaluate,
dx
2
1 x
0

(c) Describe Secant method and use it to solve 3
x 5x 1 0
07
in (0,1).
Q.5 (a) State the Gauss seidel method for laplace equation
03
1

---

(b)
2
u
u
04
Solve heat equation
with u(x,0)=0, u(0,t)=0 and
2
t
x
1
1
u(1,t)=t. with k
and h .
8
4

(c) State the Taylors method and solve equation,
07
dy
2x
y
y(0)=1.
dx
y



Q.6 (a) State the finite difference quotients for first and second
03
order derivatives.

(b) Solve y"+y+1=0 with y(0)=0, y(1)=0, Using h=0.5
04
implement finite difference approach.

(c) State the Picards formula and solve the equation for x=0.2,
07
dy
2
x y y(0)=1.
dx
Q.7 (a) Discuss the difference between finite difference and finite
03
element approach

(b) Describe the Rayleigh Ritz method in brief.
04

(c) Solve using Runge Kutta 4th order method
07
dy x y y(0)=1using h=0.05 for y(0.1).
dx



Q.8 (a) Discuss the shooting approach for boundary value
03
problems.
(b) Describe the Galerikin approach in brief.
04
(c) Solve using the equation using Galerikin approach,
07
y"+y=-x, 0<x<1 and y(0)=y(1)=0.

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