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

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

Lyapunov Instability: Example

Lyapunov Instability: Example

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

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

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

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

Evaluation accuracy stability costs conservation reversibility of time