HAX703X - Numerical analysis of hyperbolic partial differential equations
1st year M.Sc, Montpellier Faculty of Sciences, 2025
Documents
Link to all ressources on Moodle.
Contents
1) Introduction to Partial Differential Equations (PDEs)
- Definition of PDEs
- Classification: hyperbolic, elliptic, parabolic equations
2) Finite Difference methods (FD)
- Approximation of differential operators using FD methods
- Solving stationary and then time-dependent problems
- Accuracy and stability analysis
3) Analytical resolution of Scalar Conservation Laws (SCL)
- Method of characteristics
- Weak solutions
- Entropy inequality
- Riemann problems
4) Finite Volume methods (FV)
- FV methods applied to scalar conservation laws
- Godunov scheme
- Numerical fluxes
- TVD (Total Variation Diminishing) schemes
Main responsible: François Vilar