Numerical Method | BSc.CSIT (TU) Question Paper 2069 | Third Semester

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Numerical Method 2069Third Semester | Second Year | Tribhuvan University
Old Question Collection | Question Bank
Numerical Method, Year: 2069
Computer Science and Information Technology (CSc 204)
Full Marks: 60 | Pass Marks: 24 | Time: 3 hours

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[File Type: PDF | File Size: 688 KB | Download]

Candidates are required to give their answer in their own words as far as practicable.
The figures in the margin indicate full marks.

Attempt all Questions:

  1. Derive a formula to solve nonlinear equation using secant method. Using your formula estimate a real root of following nonlinear equation using secant method correct up to decimal places x2 + ln x = 3. (3+5)
  2. Estimate f(3) from the following data using Cubic Spline Interpolation. (8)
    x 1 2.5 4 5.7
    f(x) -2.0 4.2 14.4 31.2

    OR
    Find the best fitting quadratic polynomial from following data using least square approximation.

    x -2 -1.2 0 1 1.2 2.5 3 4.5 6.3
    f(x) 10.39 2.96 -2.0 -2.63 -2.46 0.83 3.1 12.8 30.4
  3. (a) For the function ?(?) =  e^x \sqrt{(sin x + ln x)} estimate ?′(6.3) and ?”(6.3) [take ℎ = 0.01] (4)
    (b) Evaluate  \int_{1}^{2} (ln x + x^2 sinx)dx using Gauss integration 3 point formula. (4)
  4. Solve the following system of linear equations using Gauss-elimination or Gauss Jordan method.
    3x1 + 5x2 – 3x3 + x4 = 16
    2x1 + x2 + x3 + 4x4 = 9
    43 – 4x2 – x4 = 1
    2x1 + x2 – 3x3 + 9x4 = 5                                                                                                                                       (8)
  5. How can you solve higher order differential equation? Explain. Solve the following differential within 0 ≤ ? ≤ 1 using Heun’s method. (3+5)
     \frac{d^2 y}{ dx^2} + 3 \frac{d y}{d x} + 2xy = 1 with ?(0)=1 and ?′(0)=1 [?ake ℎ=0.5]
  6. (a) How can you obtain numerical solution of a partial differential equation? Explain. (3)
    (b) The steady state two dimensional heat-flow in a metal plate is defined by  \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} =0. Given the boundary conditions as sown in figure below, find the temperatures at interior points T1, T2, T3 and T4. (5)NM q.n 6b figure
  7. Write an algorithm and C-program code to solve non-linear equation using Newton’s method. Your program should read an initial guess from keyboard and display the following if the solution is obtained.
    • Estimated root of the equation
    • Functional value at calculated root
    • Required number of iterations                                                                                                                                   (5+7)
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