PTU B.Tech Aerospace Engineering 4th Semester May 2019 60512 NUMERICAL ANALYSIS Question Papers

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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

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M.Code : 60512

Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.

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3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

1. Answer briefly :
   1. Find the absolute error if X = 0.00545828 is truncated to three decimal digits.
   2. What is the order of convergence in Newton-Raphson method?
   3. Find a double root of the equation 5x² + 8x-4=0 which is near 1.8.

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   4. What is Lagrange's interpolation formula?
   5. Find y'(0) from the following table :
      x: 0 1 3 4 5
      y: 4 8 15 7 6 2
   6. Solve the equations x + y = 2 and 2x + 3y = 5 using Gauss elimination method.

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   7. What is the difference between direct and iterative method of solving simultaneous linear equations method?
   8. if dy/dx = x + y, y(0) = 1, and y(1) =1+x+x² / 2 then what is the value of y⁽²⁾(x) using Picard's method?
   9. Write Milne's corrector formula.
   10. What is the standard 5-point formula to solve the Laplace equation U_xx + U_yy = 0?

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SECTION-B

2. If r = h(4h – 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
   

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   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 :
   

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   3x + 2y +7z =4; 2x + 3y + z = 5; 3x + 4y + z = 7.

SECTION-C

7. Using Runge Kutta method of order 4, find y for x = 0.1, 0.2, 0.3 given that
   dy/dx = xy + y², y(0) = 1.
   Continue the solution at x = 0.4 using Milne's method.

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8. Find the largest eigen value and the corresponding eigen vector of the matrix,
   

   2	5	1
   1	3	0
   2	0	-4

   Take [1 0 0] as initial eigen vector.
9. Solve the Laplace equation u_x + u_y = 0 in the domain of the following figure by Jacobi's method.
   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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