University of Kasdi Merbah Ouargla
Faculty of New Technologies of Info & Communication
Department of Computer Science & Info Technology
3ING Informatics
Academic year: 2024/2025
Duration: 45m
TEST ”Numerical Analysis 2”
Exercise 1
Consider the ordinary differential equation
⎧
⎪𝑥 ′ = (𝑡𝑥)3 − (𝑥/𝑡)2
⎨
⎪𝑥(1) = 1
⎩
Apply Second order Runge-Kutta method with ℎ = 0.1 to compute 𝑥(1.1).
Exercise 2
1. Consider the integral
3
 𝑥 6 − 𝑥 2 sin(2𝑥) 𝑑𝑥 = 317.3442466.
1
Approximate the following integrals using Gaussian quadrature with 𝑛 = 2, and compare your results to the exact values of the integrals.