Numerical methods (05_XBNUM)

• Coefficient : 3.5
• Hourly Volume: 80h (including 45h supervised)
  CTD : 27h supervised (and 4.5h unsupervised)
  Labo : 18h supervised (and 3h unsupervised)
  Out-of-schedule personal work : 27.5h

AATs Lists

Description

1. Differential equations and systems
   • Cauchy-Lipschitz theorem
   • Definition, convergence and order of a numerical method
   • A-stability of a numerical method
2. Linear systems:
   • Conditioning
   • Jacobi and Gauss-Seidel methods
   • Gradient methods
3. Nonlinear equations
   • Substitution methods
   • Newton–Raphson method

Learning Outcomes AAv (AAv)

• AAv1 [heures: 40, B3,B4] : at the end of this course, each student knows how to solve any differential problem using a numerical method and characterize the properties of this method.

• AAv2 [heures: 20, B3,B4] : at the end of this course, each student of semester 5 knows how to solve any linear system using an iterative numerical method adapted to the context, by formally ensuring the convergence of this last.

• AAv3 [heures: 20, B3,B4] : at the end of this course, each student knows how to solve an equation or a non-linear system using a numerical method, while formally ensuring the convergence of the latter.

Assessment methods

The evaluation is done by a long evaluation, the average of several short assessments of CTD (coefficient 1) and lab (coefficient 1)

Key Words

Numerical resolution of equations and differential systems. Numerical resolution of linear and nonlinear systems using the fixed point principle.

Prerequisites

Undergraduate linear algebra program, first year post-baccalaureate analysis program.

Resources

Lascaux et Théodor : introduction à l’analyse numérique