Documents

Lecture notes: Notes

Exercise sheets:

• TD1 - Cauchy problem, Euler & Runge schemes (Worksheet & Solutions)
• TD2 - Multistep schemes & stiff equations (Worksheet & Solutions)

Pratical works:

• TP1 - Geometrical interpretation of an ODE and Euler scheme (Worksheet & Solutions)

Contents

1) Introduction to Cauchy problems for ordinary differential equations

• Numerical methods for solving differential equations
• One-step methods: Euler, Runge-Kutta, error analysis, convergence
• Multistep methods: Adams, BDF, stability considerations
• Stiff problems and stability supplements

2) Introduction to partial differential equations

• First-order linear PDEs: constant coefficients, characteristics, conservation laws
• Finite difference methods: discretization principles, upwinding, stability, and other schemes
• Diffusion equations: heat equation, convolution solution, Fourier series, finite difference discretization
• Higher dimensions: Poisson equation