1. Introduction to Scientific Computing II
Molecular Dynamics – Discretisation
Dr. Miriam Mehl

2. Properties of the Model
reversibilty in time
H-theorem
Loschmidt objection
Lyapunov instability

3. Lyapunov Instability: Example

4. Lyapunov Instability: Example

5. Time Discretisation – Euler
position: implicit Euler
velocity: explicit Euler
combination:

6. Time Discretisation – Störmer Verlet
Taylor series
forward and backward direction
velocity-free formula

7. Time Disc. – Velocity Störmer Verlet
position: Taylor series (2nd order)
velocities: Crank Nicolson

8. Time Discretisation – Leapfrog
position: Taylor series (2nd order)
velocities: Crank Nicolson

9. Evaluation
accuracy
stability
costs
conservation
reversibility of time