Analysis and numerical methods

The aim of this module is to introduce the fundamental concepts and principles of numerical methods.
This will enable you to adapt the right approach when using a potentially complex calculation code.

- Quadrature: principle, elementary and compound formulas, order of a compound method and implications, classical and Gauss-Legendre formulas.
This chapter is also an opportunity to learn about machine errors and to discuss the efficiency of a method.
- Ordinary Differential Equations: first-order systems, existence and uniqueness (Cauchy-Lipschitz), basic numerical schemes, Runge-Kutta schemes, adaptive-step schemes, stability of a numerical scheme, parameter dependence.
Practical exercises illustrate each chapter.

Engineering Sciences and Techniques