PTU Punjab Technical University B-Tech May 2019 Question Papers 4th Semester Aerospace Engineering
Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Aerospace Engg.) (2012 Onwards)/B.Tech.(ANE) (Sem.?4)
NUMERICAL ANALYSIS
Subject Code : ANE-204
M.Code : 60512
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3.
SECTION-C contains T HREE questions carrying T EN marks each and students
have to attempt any T WO questions.
SECTION-A
1.
Answer briefly :
(a) Find the absolute error if X = 0.00545828 is truncated to three decimal digits.
(b) What is the order of convergence in Newton-Raphson method?
(c) Find a double root of the equation x3 ? 5x2 + 8x ? 4 = 0 which is near 1.8.
(d) What is Lagrange's interpolation formula?
(e) Find y'(0) from the following table :
x : 0
1
2
3
4
5
y : 4
8
15
7
6
2
(f) Solve the equations x + y = 2 and 2x + 3y = 5 using Gauss elimination method.
(g) What is the difference between direct and iterative method of solving simultaneous
linear equations method?
dy
(h)
(1)
2
if
x y, y(0) 1, and y
1 x x / 2 then what is the value of y(2)(x) using
dx
Picard's method?
(i) Write Milne's corrector formula.
(j) What is the standard 5-point formula to solve the Laplace equation Uxx + Uyy = 0?
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SECTION-B
2.
If r = h(4h5 ? 5), find the percentage error in r at h = 1 if the error in h is 0.04.
3.
Apply iteration method to find the negative root of the equation x3 ? 2x + 5 = 0 correct to
four decimal places.
4.
Find f(22) from the Gauss forward formula :
x :
20
25
30
35
40
45
f(x) : 354
332
291
260
231
204
5.
Find the maximum and minimum value of y from the following table :
x :
-2 -1 0
1
2 3
4
y :
2 -0.25 0 -0.25
2 15.75
56
6.
Apply factorization method to solve the equations :
3x + 2y +7z =4; 2x + 3y + z = 5; 3x + 4y + z = 7.
SECTION-C
Q7. Using Runge Kutta method of order 4, find y for x = 0.1, 0.2, 0.3 given that
dy
2
xy y , y(0) 1. Continue the solution at x = 0.4 using Milne's method.
dx
Q8. Find the largest eigen value and the corresponding eigen vector of the matrix,
25 1
2
1
3
0 . Take [1 0 0]t as initial eigen vector.
2 0
4
Q9. Solve the Laplace equation uxx + uyy = 0 in the domain of the following figure by Jacobi's
method.
1
1
0
0
4
3
0
0
1
2
0
0
Fig.1
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 04 November 2019