CACS252 Numerical Method

Numerical Method TU Board 2024 question paper

10 questionsSit this paper (timed)

Tribhuvan University

Bachelor of Computer Application

Semester 4 · TU Board 2024

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 A

    Group B

    Attempt any SIX question.(6 × 5 = 30)

    1. 2.

      Explain absolute and relative error. Find the relative error of number 5.6 if both of its digits are correct.

      5
    2. 3.

      On what type of equations Newton's methods can be applicable. Justify.

      5
    3. 4.

      Solve the following equations by using Gauss-Jordan method. 2x+3y+4z=5   3x+4y+5z=6  4x+5y+6z=7

      5
    4. 5.

      Use the Romberg method to get an improved estimate of the integral from x = 1.8 to x = 3.4 from the data in the table with h = 0.4.X :1.61.82.02.22.42.62.83.03.23.43.63.8Y4.956.057.389.0211.0213.4616.4420.0524.5329.9636.5944.70:309534563481

      5
    5. 6.

      Write a program to compute integral _0∫^x/2 √sinx dx Simpson's 1/3 rule.

      5
    6. 7.

      Using Runge-Kutta method of 4th order solve the following equation taking each step h = 0.1 dydx=4xy - xy given y(0) = 3.3 calculate y at x = 0.1 and 0.2.

      5
    7. 8.

      Solve the laplace equation Uxx + Uyy = 0 for the following square mesh with the boundary values.

      5

    Group C

    Attempt any TWO questions(2 × 10 = 20)

    1. 9.

      Solve the given set of linear equations using Dolittle LU decomposition method:   3x _1 + 2x _2 + x _3 = 10   2x _1 + 3x _2 + 2x _3 = 14   3x _1 + 2x _2 + 3x _3 = 14

      10
    2. 10.

      Define initial value problems and final value problems. Using heun's method, find value of y when x=0.3 given that dydx = x + y and y=1 when x=0.

      10
    3. 11.

      How can x we use Laterpolation techniques (methods) to approximate the value of the integral for the functions whose antiderivative can't be found? Explain. Write a program to solve sin x - 2x + 1 = 0 using Bisection method.

      10

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