En hurtig implementation af Eulers metode til numerisk løsning af koblede differentialligninger, til brug i min SRP

euler_numerical_solver.js

/**
 * PLEASE READ:
 * This is a very simple implementation of Eulers method for
 * numerically solving coupled differential equations, used
 * in an article of mine. It outputs the data in a CSV format
 * (which is plaintext).
 * 
 * To run the code, press F12, go to the Console tab of the window
 * that opens, and paste the code (that's everything with the
 * line numbers, as seen to the left, beside it) in there. 
 * A textbox should appear on the website (in the middle), which 
 * contains your data. The easiest way to copy this data is to
 * click the textbox, then CTRL+A (or CMD+A if you're on a Mac)
 * and then CTRL+C (or CMD+C).
 * 
 * To plot this data, paste it into
 * Notepad and save as <somename>.csv. Then open this file with
 * Excel and do "Insert > Scatterchart" (punktdiagram in Danish)
 * 
 * The step size is set to 0.01, and the interval is [0;10].
 * This gives us 1000 data points, and a small enough step size to
 * be relatively exact.
 */

// JS isn't good with tiny numbers, so we do all calculations 
// (eg. division with mass) beforehand
var g = -9.82;
var bPrM = 0.002185;
var cPrM = 0.2033;

function dX(x,y){
  return -bPrM * x - cPrM*Math.sqrt(x*x+y*y)*x;
}
function dY(x,y){
  return g - bPrM * y - cPrM*Math.sqrt(x*x+y*y)*y;
}

var data = Euler(dX,dY,8.845,1.946,0,10,.01);
var outp = '"t";"Vx";"Vy"\n';
for (var i = 0; i < data.x.length; ++i) {
  outp += (data.x[i][0]+"").replace(".",",")+
            ";"+
          (data.x[i][1]+"").replace(".",",")
            +";"+
          (data.y[i][1]+"").replace(".",",")
            +"\n";
}
var t = document.createElement("textarea");
document.body.appendChild(t);
t.value = outp;
t.style.position = "fixed";
t.style.top = "50%";
t.style.left = "50%";
t.style.zIndex = "9999999";
t.style.boxShadow = "0 0 0 100vw rgba(0,0,0,.5)";
t.style.transform = "translate(-50%,-50%)";

/**
 * Numerically solve coupled differential functions
 * Func1 and func2 are called with
 *   (val1, val2)
 */
function Euler(func1,func2,start1,start2,minVar,maxVar,stepVar){
  var points1 = [];
  var points2 = [];
  var t = minVar;
  var p1 = [t,start1];
  var p2 = [t,start2];
  points1.push(p1);
  points2.push(p2);
  
  // we have our starting point
  // loop until we've reached end
  while (t < maxVar) {
    p1 = getNext(p1, stepVar, func1, p1[1],p2[1]);
    p2 = getNext(p2, stepVar, func2, p1[1],p2[1]);
    points1.push(p1);
    points2.push(p2);
    
    t += stepVar;
  }
  
  return {"x": points1, "y": points2};
}
function getNext(prevP, stepVar, func,val1,val2) {
  var a = getAngle(func,val1,val2);
  console.log("Got angle",func,a,prevP[0]);
  return [
    prevP[0] + stepVar,
    prevP[1] + stepVar*a
  ];
}
function getAngle(func,val1,val2) {
  return func(
    val1,
    val2
  );
}