// program by (c) J-P Moreau E-mail:  jpmoreau@wanadoo.fr
// home page http://perso.orange.fr/jean-pierre.moreau/cplus.html

// globals:

var theTestFunx = 'x*y + cos(t) - 0.5*sin(2*t)';
var theTestFuny = 'x^2 + y^2 - (1 + sin(t))';

function displayResults() {
// var theScriptString = '<STYLE TYPE=' + quoteMark + 'text/css' + quoteMark + '>BODY, LAYER, P, DIV, TABLE, TR, TD, TH {font-size: 12px; font-family: times; color: 000000}</STYLE>';

var theString = '<center><TABLE BORDER = 1 cellspacing = 0 cellpadding = 2 noshade border = 0 bordercolor = #FF7272 STYLE="background-color: FFE9EE; border-collapse: collapse"><tr>';
for (var j = 1; j <= numCurves; j++) {
	theString += '<td align = center><i>t</i></td><td align = center><i>x</i></td><td align = center><i>y</i></td>';
	} // j

theString += '</tr><tr>';

for (var i = 0; i <= numPoints; i++) {
	for (var j = 1; j <= numCurves; j++) {
		theString+= '<td>' + roundSigDig(theCombinedResult[j][1][i],8) + '</td>';
		theString+= '<td>' + roundSigDig(theCombinedResult[j][2][i],8) + '</td>';
		theString+= '<td>' + roundSigDig(theCombinedResult[j][3][i],8) + '</td>';
		} // j
	theString += '</tr>'
	} // i
theString += '</table></center>';
document.getElementById("data").innerHTML = theString;



//var tb="toolbar=0,directories=0,status=0,menubar=0"
//tb+=",scrollbars=1,resizable=1,"
//var tbend="width=500,height=500";
//tb+=tbend;
//var Win_1 = window.open("","win1",tb);
//Win_1.document.write(theString);
//Win_1.document.close();
//Win_1.focus();
}


function RungeKutta2(xFunc, yFunc, x0, y0, tStart, tEnd, numSteps) {
// will return a two dim array [1, t] = value of t, [2, t] = value of x(t)
// [3, t] = value of y[t]
numPoints = numSteps;  // set the global
var theResult = new makeArray2(3, numSteps+1); // cusion for extra coord
var h = (tEnd - tStart)/numSteps;
var h2 = h/2;
theResult[1][0] = parseFloat(tStart);
theResult[2][0] = parseFloat(x0); // initial value
theResult[3][0] = parseFloat(y0);
t = tStart;
var x1 = 0, y1= 0, c1= 0, d1= 0, c2= 0, d2= 0, c3= 0, d3= 0;
for (k = 0; k < numSteps; k++) {
// RK4(X[k],Y[k],Z[k],h,&X[k+1],&Y[k+1],&Z[k+1]);
	x = theResult[2][k];
	y = theResult[3][k];
	x1 = theResult[2][k];
	y1 = theResult[3][k];
	c1 = myEval(xFunc); 
	d1 = myEval(yFunc); 
	t+=h2; x = x1+h2*c1; y = y1 + h2*d1;
	c2 = myEval(xFunc); 
//alert("x = " + x + " y = " + y + "t = " + t + "c2 = " + c2);
	d2 = myEval(yFunc);
	x = x1+h2*c2; y = y1 + h2*d2;
	c3 = myEval(xFunc);
	d3 = myEval(yFunc);
	t += h2; x = x1+h*c3; y = y1 + h*d3;
	c4 = myEval(xFunc);
	d4 = myEval(yFunc);
	theResult[1][k+1] = t;
	theResult[2][k+1] = x1 + h*(c1+2*c2+2*c3+c4)/6;
	theResult[3][k+1] = y1 + h*(d1+2*d2+2*d3+d4)/6;
	}  // k
return(theResult);
} // RungeKutta2