jeremyckahn/gist:1289158

## gistfile1.html
<html>

<head>
</head>

<body>

<script>

function State () {
  this.x = null;
  this.v = null;
  return this;
}

function  Derivative () {
  this.dv = null;
  this.dx = null;
  return this;
}

function  acceleration (state, t) {
  var k = 10,
      b = 1;

  return - k*state.x - b*state.v;
}

/**
 * @param {State} initial
 * @param {number} t
 * @param {number} dt
 * @param {Derivative} d
 */
function evaluate (initial, t, dt, d) {
  var state = new State();
  var output = new Derivative();

  if (typeof dt === 'undefined') {
    output.dx = initial.v;
    output.dv = acceleration(initial, t);
  } else {
    state.x = initial.x + d.dx*dt;
    state.v = initial.v + d.dv*dt;

    output.dx = state.v;
    output.dv = acceleration(state, t+dt);
  }

  return output;
}

function integrate (state, t, dt) {
  var a = evaluate(state, t),
      b = evaluate(state, t, dt*0.5, a),
      c = evaluate(state, t, dt*0.5, b),
      d = evaluate(state, t, dt, c);

  var dxdt = 1/6 * (a.dx + 2 * (b.dx + c.dx) + d.dx);
  var dvdt = 1/6 * (a.dv + 2 * (b.dv + c.dv) + d.dv);

  state.x += dxdt*dt;
  state.v += dvdt*dt;
}

(function () {
  var state = new State();
  state.x = 100;
  state.v = 0;

  var t = 0;
  var dt = 0.1;

  while (Math.abs(state.x) > .001 || Math.abs(state.v) > .001) {
    console.log(state.x, state.v);
    integrate(state, t, dt);
    t += dt;
  }
} ());

</script>

</body>
</html>
	<html>

	<head>
	</head>

	<body>

	<script>

	function State () {
	this.x = null;
	this.v = null;
	return this;
	}

	function Derivative () {
	this.dv = null;
	this.dx = null;
	return this;
	}

	function acceleration (state, t) {
	var k = 10,
	b = 1;

	return - kstate.x - bstate.v;
	}

	/**
	* @param {State} initial
	* @param {number} t
	* @param {number} dt
	* @param {Derivative} d
	*/
	function evaluate (initial, t, dt, d) {
	var state = new State();
	var output = new Derivative();

	if (typeof dt === 'undefined') {
	output.dx = initial.v;
	output.dv = acceleration(initial, t);
	} else {
	state.x = initial.x + d.dx*dt;
	state.v = initial.v + d.dv*dt;

	output.dx = state.v;
	output.dv = acceleration(state, t+dt);
	}

	return output;
	}

	function integrate (state, t, dt) {
	var a = evaluate(state, t),
	b = evaluate(state, t, dt*0.5, a),
	c = evaluate(state, t, dt*0.5, b),
	d = evaluate(state, t, dt, c);

	var dxdt = 1/6 * (a.dx + 2 * (b.dx + c.dx) + d.dx);
	var dvdt = 1/6 * (a.dv + 2 * (b.dv + c.dv) + d.dv);

	state.x += dxdt*dt;
	state.v += dvdt*dt;
	}

	(function () {
	var state = new State();
	state.x = 100;
	state.v = 0;

	var t = 0;
	var dt = 0.1;

	while (Math.abs(state.x) > .001 \|\| Math.abs(state.v) > .001) {
	console.log(state.x, state.v);
	integrate(state, t, dt);
	t += dt;
	}
	} ());

	</script>

	</body>
	</html>