Euler

You will find this code in the EJS console at page Initialization.

lines marked //  include remarks that do not influence the calculation.

xE[0]=0;

yE[0]=valueFrom;

derivativeE[0]=yE[0];//for exponential

for (var i=1; i<n; i++) {//loop definitionn)

xE[i]=xE[i-1]+delta;

yE[i]=yE[i-1]+delta*derivativeE[i-1];

derivativeE[i]=yE[i];//for exponential

//back to start of loop

FE[i]=(valueFrom*Math.exp(xE[i])-yE[i])/(valueFrom*Math.exp(xE[i]));

}

Heun

xH[0]=0;

yH[0]=valueFrom;

derivativeH_a[0]=yH[0];//for exponential

for (var i=1; i<n; i++) {//loop definition)

xH[i]=xH[i-1]+delta;

yH_a[i]=yH[i-1]+delta*derivativeH_a[i-1];

derivativeH_b[i]=yH_a[i];////for exponential

yH[i]=yH[i-1]+delta/2*(derivativeH_a[i-1]+derivativeH_b[i]);

derivativeH_a[i]=yH[i];////for exponential

//back to loop

FH[i]=(valueFrom*Math.exp(xH[i])-yH[i])/(valueFrom*Math.exp(xH[i]));

}