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)
- 2.5
Explain absolute and relative error. Find the relative error of number 5.6 if both of its digits are correct.
- 3.5
On what type of equations Newton's methods can be applicable. Justify.
- 4.5
Solve the following equations by using Gauss-Jordan method. 2x+3y+4z=5 3x+4y+5z=6 4x+5y+6z=7
Answer comingAlso asked in 2026, 2025, 2023, 2020
- 5.5
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
- 6.5
Write a program to compute integral _0∫^x/2 √sinx dx Simpson's 1/3 rule.
- 7.5
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.
- 8.5
Solve the laplace equation Uxx + Uyy = 0 for the following square mesh with the boundary values.
Group C
Attempt any TWO questions(2 × 10 = 20)
- 9.10
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
- 10.10
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.
- 11.10
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.
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