//OurFunction.js
//Global variable
var yInitial = 1;
var steps = 0.25;
var xMaximum = 2;
var n = xMaximum/steps;

//Function eulerMethod()
function eulerMethod()
{
    //Declare variables
    var xVal,yVal,hVal,tVal,kVal;

    //Initialize
    xVal=0;
    yVal=yInitial;
    hVal= steps;
    tVal=xMaximum;

    //Loop
    while(xVal<=tVal)
    {
        //Compute
        kVal=hVal*logic(xVal,yVal);
        yVal=yVal+kVal;
        xVal=xVal+hVal;
    }

    //Write output
    document.write("Euler method result: "+yVal);
}

//Function heunsMethod()
function heunsMethod()
{
    //Declare variables
    var xVal,yVal,hVal,tVal,kVal;

    //Initialize
    xVal=0;
    yVal=yInitial;
    hVal=steps;
    tVal=xMaximum;

    //Loop
    while(xVal+hVal<=tVal)
    {
        //Compute
        l=(hVal/2)*(logic(xVal,yVal)+logic(xVal+hVal,yVal+hVal*logic(xVal,yVal)));
        yVal=yVal+l;
        xVal=xVal+hVal;
    }

    //Write output
    document.write("Heuns method result: "+yVal);
}

//Function rungekutta4()
function rungekutta4()
{
    //Declare variables
    var k1,k2,k3,k4,m=0,yVal,xVal,hVal,tVal;

    //Initialize
    xVal=0;
    yVal=yInitial;
    hVal=steps;
    tVal=xMaximum;

    //Loop
    while(xVal<tVal)
    {
        //Compute
        k1=logic(xVal,yVal);
        k2=logic((xVal+hVal/2.0),(yVal+k1*hVal/2.0));
        k3=logic((xVal+hVal/2.0),(yVal+k2*hVal/2.0));
        k4=logic((xVal+hVal),(yVal+k3*hVal));
        m=((k1+2*k2+2*k3+k4)/6);
        yVal=yVal+m*hVal;
        xVal=xVal+hVal;
    }

    //Write output
    document.write("Runge kutta 4th order result: "+yVal);
}

//Function rungekutta3()
function rungekutta3()
{
    //Declare variables
    var k1,k2,k3,m=0,yVal,xVal,hVal,tVal;

    //Initialize
    xVal=0;
    yVal=yInitial;
    hVal=steps;
    tVal=xMaximum;

    //Loop
    while(xVal<tVal)
    {
        //Compute
        k1=logic(xVal,yVal);
        k2=logic((xVal+hVal/2.0),(yVal+k1*hVal/2.0));
        k3=logic((xVal+hVal),(yVal-k2*hVal+2.0*k2*hVal));
        m=((k1+4*k2+k3)/6);
        yVal=yVal+m*hVal;
        xVal=xVal+hVal;
    }

    //Write output
    document.write("Runge kutta 3rd order result: "+yVal);
}

//Method logic()
function logic(xVal,yVal)
{
    //Declare variable
    var func;

    //Compute
    func= yVal*xVal*xVal - 1.2*yVal;

    //Return
    return func;
}