Run it yourself

Projectile with drag

The solver from the slides, running here. Change what you are throwing, how hard, and how finely the solver walks through time. Nothing is precomputed: every line on this page is integrated in the browser when you move a control.

function rate(u: State, k: number): State {
  const [, , vx, vy] = u;
  const speed = Math.hypot(vx, vy);
  return [vx, vy, -k * speed * vx, -G - k * speed * vy];
}

const rk4Step: Stepper = (u, h, k) => {
  const a = rate(u, k);
  const b = rate(add(u, a, h / 2), k);
  const c = rate(add(u, b, h / 2), k);
  const d = rate(add(u, c, h), k);
  return u.map((ui, i) =>
    ui + (h / 6) * (a[i] + 2 * b[i] + 2 * c[i] + d[i]));
};

Same twelve lines either way. The physics is in rate, the numerics is in the stepper, and the choice of language is the least interesting decision in the file.