Download PTU B-Tech AR-Automation-And-Robotics 2020 Dec 5th Sem 70482 Numerical Methods In Engineering Question Paper

Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (AR)- Automation-And-Robotics 2020 December 5th Sem 70482 Numerical Methods In Engineering Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 18
B.Tech (Automation & Robotics) (2011 & Onwards) (Sem.?5)
NUMERICAL METHODS IN ENGINEERING
Subject Code : ME-309
M.Code : 70482
Time : 3 Hrs. Max. Marks : 60
INST RUCT IONS T O CANDIDAT ES :
1 .
SECT ION-A is COMPULSORY cons is ting of TEN questions carrying TWO marks
each.
2 .
SECT ION-B c ontains F IVE questions c arrying FIVE marks eac h and s tud ents
have to atte mpt ANY FOUR questio ns.
3 .
SECT ION-C contains THREE questions carrying T EN marks e ach and s tudents
have to atte mpt ANY TWO questions .
SECTION-A
Answer the following :
1.
Define a cubic spline interpolant with natural boundary.
2.
What do we mean by unconditionally stable method?
3.
Find the condition number of the function f(x) = cos x.
4.
Determine the Lagrange interpolating polynomial passing through the points (2,4) and
(5,3).
5.
Out of chopping of numbers and rounding off of numbers, which one introduce less
error? Explain suitably.
6.
Find the l
t
2 norm of the vector (1,
6, 3) .
7.
What is the order of convergence when Newton Raphson's method is applied to the
equation x2 ? 6x + 9 = 0 to find its multiple root.
8.
Use the forward-difference formula to approximate the derivative of f(x) = ln x at x0 = 1.8
using h = 0.01.
9.
Compute
x sin xdx using Simpson's rule.
0
10. Explain Lagrange's interpolation.
1 | M -70482
(S2)-959

---

SECTION-B
11.
Use Euler's method to approximate the solution of the following initial value problem
y' = y/t ? (y/t)2, l t 2, y(l) = 1, h = 0.1.
12.
Construct a clamped spline S(x) which passes through the points (1,2), (2,3) and (3,5) that
has S'(l) = 2 and S'(3) = 1.
13.
The following data is given :
1.0
1.3
1.6
1.9
2.2
0.7651977
0.6200860
0.4554022
0.2818186
0.1103623
Use Lagrange's formula to approximate f(1.5).
14.
Let f(x) = (x cos x ? sin)/(x ? sin x). Use four digit rounding arithmetic to evaluate f(0.1).
The actual value is f(0.1) = ?1.99899998, using this value find the relative error.
15.
Use backward-difference method with steps sizes h = 0.1 and k = 0.01 to approximate the
solution to the heat equation
2
u
u
(x,t)
( x,t) 0, 0 x 1, t 0,
2
i
x
with boundary conditions u(0,t) c(1,t) 0, t 0,
u( ,
x 0) sin( x
), 0 x 1.
SECTION-C
16.
Determine the values of h that will ensure an approximation error of less than 0.00002
when approximating
sin xdx and employing.
0
a) Composite trapezoidal rule.
b) Composite Simpson's rule.
17.
Draw the graph of 4x = tan x. Use Newton's method to find the first two positive roots of
4x = tan x (Note: You can use the graph drawn for selecting your initial guesses.).
18.
Use Gauss elimination method with scaled partial pivoting to solve the following linear
system of equations
2.11x1 ? 4.21x2 + 0.921x3 = 2.01,
4.01x1 + 10.2x3 ? 1.12x3 = ? 3.09,
1.09x1 + 0.987x2 + 0.832x3 = 4.21.
NOTE : Disclosure of identity by writing mobile number or making passing request on any
page of Answer sheet will lead to UMC case against the Student.
2 | M -70482
(S2)-959

---