CACS252 Numerical Method

Numerical Method TU Board 2023 question paper

10 questionsSit this paper (timed)

Tribhuvan University

Bachelor of Computer Application

Semester 4 · TU Board 2023

Course Title: Numerical Method (CACS252)

Full Marks: 60Pass Marks: 24Time: 3 hours

Candidates are required to answer the question in their own words as far as possible.

Group B

Attempt any SIX question.(6 × 5 = 30)

  1. 2.

    Define error. Explain the Taxonomy Errors.

    5
  2. 3.

    Estimate the value of sin θ at 9 = 45° using Newton's backward difference formula from the following set of data.θ102030405060Sin θ0.17360.34200.50000.64280.76600.8660

    5
  3. 4.

    Write an algorithm and program to calculate integration using Trapezoidal rule.

    5
  4. 5.

    What is the form of resultant matrix using Gauss-Jordan method? Solve the following system of equations using Gauss-Jordan Method. x + 2y - 3z = 4 2x + 4y - 6z = 8 x - 2y - 5z = 4

    5
  5. 6.

    Define ordinary differential equation. Use the fourth order Runge-Kutta method to estimate y(0.4) of the equation: dydx=x2+y2 with y(0) = 0 assuming that h = 0.2

    5
  6. 7.

    Solve for the steady state temperatures in a rectangular plate of 8cm x 10cm, if one 10cm side is held at 50°C, and the other 10cm side is held at 30°C and other two sides are held at 10°C. Assume grids of size 2cm x 2cm.

    5
  7. 8.

    Write a short note on (Any Two): a) Partial Differential Equations b) Linear Interpretation c) Boundary value problems

    5

Group C

Attempt any TWO questions(2 × 10 = 20)

  1. 9.

    Write an algorithm and program to compute the root of nonlinear equation using Newton - Raphson method.

    10
  2. 10.

    a) Fit a straight line to the following set of data using Least Square Regression. b) Apply the factorization method (any) to solve the equations: 2x + 3y + 7z = 4 2x + 3y + z = 5 3x + 4y + z = 7

    10
  3. 11.

    a) Write and implement an algorithm to solve the system of linear equations using Gauss-Seidel method with suitable example. b) Write a program to solve the ordinary differentia; equations using Heun's method.

    10

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