Numerical methods

(NUM)

• Coefficient : 1.5
• Hourly Volume: 31.5h (including 18.75h supervised)
  CTD : 8.75h supervised (and 2.5h unsupervised)
  Labo : 10h supervised (and 1.25h unsupervised)
  Out-of-schedule personal work : 9h

AATs Lists

Description

1. Reminders on differential equations
2. Numerical methods ( Convergence, stability )
3. Simulation in Python

Learning Outcomes AAv (AAv)

• AAv1 [heures: 30, B3, B4] : at the end of this course, each student will be able to solve any differential problem using a numerical method and to characterise the properties of this method. This solution and characterisation are satisfactory if:
  • any differential problem is reduced to a first-order problem ;
  • the problem is solved numerically using algorithms which may or may not be pre-coded;
  • the numerical data resulting from the solution is used;
  • the order of a given method is calculated formally and estimated numerically;
  • the absolute stability radius of a given method is calculated and used on any differential system.

Assessment methods

One long continuous assessment (coefficient 1) and the average of several short continuous assessments in CTD (coefficient 1) and Lab (coefficient 1).

Key Words

Euler method, stability

Prerequisites

Analytical solution of differential equations. Limited expansion. Numerical sequences.

Resources

J.P. DEMAILLY, Analyse numérique et équations différentielles, presse universitaire de Grenoble