Tribhuvan University BSc Third Year Numerical Methods Exam Question 2081

Tribhuvan University · Numerical Methods (BSc Third Year) · 2081 BS · Annual Examination — Elective, New Course — 6 questions — a free old question paper on Goodone.club’s exam-paper archive.

  1. Define error in numerical methods and describe its different kinds. If the number 625.4835 is approximated to 4 significant digits, find the percentage error in the number. [2+2] OR Write a MATLAB program to solve the initial-value problem y′ = f(x, y), y(x₀) = y₀ at x = xₚ using the RK-2 method with step size h. [4] [4 marks]
  2. Solve the following system of linear equations using the LU-decomposition method: x + y + z = 9; 2x − 3y + 4z = 13; 3x + 4y + 5z = 40. OR Write the algorithm of the Gauss elimination method for solving the linear system Ax = b. [7] [7 marks]
  3. Find the value of y(3) from the following data using the Lagrange interpolation formula: x = 1, 4, 9, 11 and y = 10, 25, 40, 60. [6] [6 marks]
  4. Find a real root of the equation 3x = cos x + 1 using the secant method, correct to four decimal places. [6] [6 marks]
  5. Use Simpson's 1/3 rule to evaluate ∫₀² e^(−x²) dx, taking a suitable number of subintervals. [6] [6 marks]
  6. Given the initial-value problem dy/dx = x + sin y, y(0) = 1, use Euler's method to find y at x = 1. Take h = 0.1. [6] [6 marks]