Numerical Method | BSc.CSIT (TU) Question Paper 2067 | Third Semester

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NM 2067 Third Semester | Second Year | Tribhuvan University
Old Question Collection | Question Bank
Numerical Method, Year: 2067
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: 682 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. Discuss methods of Half Interval and Newton’s for solving the nonlinear equation f(x) = 0. Illustrate the methods by figures and compare them stating their advantages and disadvantages. (8)
  2. Derive the equation for Lagrange’s interpolating polynomial and find the value of f(x) at x = 1 for the following: (4+4)
    X -1 -2 2 4
    F -1 -9 11 69
  3. Write Newton-cotes integration formulas in basic form for x = 1, 2, 3 and give their composite rules. Evaluate  \int_{.5}^{1.5} e^{-x^2} dx using the Gaussian integration three point formula. (4+4)
  4. Solve the following algebraic system of linear equations by Gauss-Jordan algorithm. (8)
     \begin{bmatrix}  0 & 2 & 0 & 1 \\  2 & 2 & 3 & 2 \\  4 & -3 & 0 & 1 \\  6 & 1 & -6 & -7  \end{bmatrix}  \begin{bmatrix}  x_{1} \\ x_{2} \\ x_{3} \\ x_{4}  \end{bmatrix}  =  \begin{bmatrix}  0 \\ -2 \\ -7 \\ 6 \end{bmatrix}
  5. Write an algorithm and program to solve system of linear equations using Gauss-Siedel iterative method. (4+8)
  6. Explain the Picard’s proves of successive approximation. Obtain a solution upto the fifth approximation of the equation
     \frac{dy}{dx} = y + x such that y=1 when x=0
    using Picard’s process of successive approximations. (2+6)
  7. Define a difference equation to represent a Laplace’s equation. Solve the following Laplace equation.
     \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} =0 within 0≤?≤3, 0≤?≤3.
    For the rectangular plate given as: (3+5)
    NM 2067 qn.7 graph
    OR
    Derive a difference equation to represent a Poison’s equation. Solve the Poison’s equation ∇2?=2?2?2 over the domain 0≤?≤3, 0≤?≤3 with ?=0 on the boundary and ℎ=1. (3+5)
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