Numerical Method 2019 year Question paper solution (BCA Fourth Semester) TU


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  1. Which one of the following can causes a blunders in system?
  • Human imperfection
  • Numerical Methods
  • Computing Methods
  • Measuring Methods
  1. Which one of the following be possible solution of system of linear equation with equations 2x-y = 5    and  3x-3/2y=4 ?
  • Unique Solution
  • No solution
  • Infinite Solution
  • Iii-condition
  1. In which method improved rood x1 is calculated as x0-f(x0)/f’(x0)?
  • Bisection Method
  • Secant Method
  • Newton-Raphson Method
  • False Point Method
  1. Which one of the following is not an open end method (extrapolation method) of solving non linear equattions?
  • Bisection Method
  • Newton -Raphson Method
  • Secant Method
  • Fixed Point Method
  1. Which one of the following is an iteration method of solving the system of linear equations?
  • Gauss-jardon Method
  • Matrix inverse Method
  • Trangular Factorization Method
  • Gauss-seidel Method
  1. Which of the following is a cubic splines with zero second derivatives at the end points?
  • Quadratic Splines
  • Natural cubic Splines
  • Semi-cubic Splines
  • No Splines
  1. Which one of the following is correct value of Romberg estimate R(0,0) for 1∫2 1/x dx ?
  • 70
  • 85
  • 75
  • 80
  1. Which one of the following is an Elliptic Equation?
  • Laplace Equation
  • Crank Nicolson Method
  • Bender-Schmid Equation
  • Newton-Gregory Method
  1. Which one of the following method is similar to two stage Runge Kutta Method?
  • Tayler Series Method
  • Euler’s Method
  • Picard’s Method
  • Heun’s Method
  1. Which one of the following is the correct value off eigen values for 8×1 – 4×2 = ʵx1 and 2×1 – 2×2 = ʵx2?
  • 4,5
  • 6,4
  • 8,2
  • 4,2

Group B

  1. why is the study of errors important to a computational scientist ? Differentiate between inherent and numerical errors.
  2. Find the root of equation x2 – 4x – 10 = 0 using bisection method where root lies between 5 and 6.
  3. Find the square root of 3.5 using second order Larange interpolation polynomial using the following data table.
X12345
F(x)11.41421.732122.2361
  1. Write a program to calculate the integral using Trapezoidal Rules?
  2. solve the following set of equation using Gauss-Jardon Method

3x-5y+ 2z = 15

4x – y + z = 2

X – 3y + 7z = 22

  1. Use classical Runge -Kutta Method to estimate (0.2) when y’(x) = x2 + y2  with y(0) = 0 and h = 0.2
  2. solve the poisson equation over the square domain 0 ≤ x≤ 3 and 0≤ y≤ 3 with f = 0

GROUP C

  1. a) Factroize the matrix

1   2   3

2   8   22                                Using Cholesky’s Method

22   8  2

(b) Locate the root of equation x2 + x – 2 = 0 using the fixed point method?

10 (a) Fit a straight line to the following set of data points.

X134689
y134457

(b)Differentiate between ordinary and partial differential equations with their applications

  1. Given the data points:
I012
Xi234
fi4916

Estimate the function value f at x = 2-5  using cubic splines.

Solution


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