Numerical integration

The explicit integrators behind every trajectory in this gallery: Euler’s method, Runge-Kutta, Stormer-Verlet, Dormand-Prince adaptive stepping, Yoshida’s symplectic composition, and the Adams-Bashforth multistep methods and their stability regions.

Euler’s method: first-order convergence

Euler's method: first-order convergence

Runge, Heun and Kutta: Runge-Kutta methods

Runge, Heun and Kutta: Runge-Kutta methods

Stormer-Verlet: bounded energy error over long times

Stormer-Verlet: bounded energy error over long times

Dormand-Prince: embedded pairs and adaptive step size

Dormand-Prince: embedded pairs and adaptive step size

Yoshida’s symplectic composition: fourth order from leapfrog

Yoshida's symplectic composition: fourth order from leapfrog

Bashforth and Adams: linear multistep methods

Bashforth and Adams: linear multistep methods