Numerical analysis of differential equations

Acquire basic notions of numerical methods for differential equations

This UE will cover the following points:

- Numerical methods for ODEs: Modeling, one-step method (Euler, Runge, Heun, RK4), consistency error. Scheme order and convergence. Steep problems and stability of implicit schemes. Multi-step methods. stability and convergence.

- Introduction to linear PDEs and modeling: basic concepts, 1st-order examples, classification of 2nd-order PDEs with constant coefficients. Examples of typical linear PDEs, introduction to numerical solution by finite differences, illustrated by examples.

Analysis courses in L1, L2 and the first semester of L3, in particular :

- HAX302X Analysis III Integration and elementary differential equations

- HAX502X Differential calculus and differential equations

Recommended prerequisites: first semester of L3

Hourly volumes :

            CM: 18

            TD : 15

            TP: 12

            Land: -