//
// rkckStep takes a Cash-Karp Runge-Kutta step
// to estimate the error and the substance levels
// after the attempted step.
//
private void rkckStep(double h) {
double t = timer.getTime();
// step 1
for (int i = 0; i < numberOfSubstances; i++) {
//
// get the substance values before this step
//
y1[i] = s[i].getValue();
//
// k1 = h * f(t, y);
//
k1[i] = h * s[i].getRate();
}
// step 2
//
// k2 = h * f (t + a2 * h, y + b21 * k1)
//
timer.setTime(t + a2 * h);
for (int i = 0; i < numberOfSubstances; i++) {
s[i].setValue(y1[i] + k1[i] * b21);
k2[i] = h * s[i].getRate();
}
// step 3
//
// k3 = h * f (t + a3 * h, y + b31 * k1 + b32 * k2)
//
timer.setTime(t + a3 * h);
for (int i = 0; i < numberOfSubstances; i++) {
s[i].setValue(y1[i] + b31 * k1[i] + b32 * k2[i]);
k3[i] = h * s[i].getRate();
}
// step 4
//
// k4 = h * f (t + a4 * h, y + b41 * k1 + b42 * k2 + b43 * k3)
//
timer.setTime(t + a4 * h);
for (int i = 0; i < numberOfSubstances; i++) {
s[i].setValue(y1[i] + b41 * k1[i] + b42 * k2[i] + b43 * k3[i]);
k4[i] = h * s[i].getRate();
}
// step 5
// k5 = h * f (t + a5 * h, y + b51 * k1 + b52 * k2 + b53 * k3 + b54 *
// k4)
//
timer.setTime(t + a5 * h);
for (int i = 0; i < numberOfSubstances; i++) {
s[i].setValue(y1[i] + b51 * k1[i] + b52 * k2[i] + b53 * k3[i] + b54 * k4[i]);
k5[i] = h * s[i].getRate();
}
// step 6
// k6 = h * f (t + a6 * h, y + b61 * k1 + b62 * k2 + b63 * k3 + b64 * k4
// + k65 * k5)
//
timer.setTime(t + a5 * h);
for (int i = 0; i < numberOfSubstances; i++) {
s[i].setValue(y1[i] + b61 * k1[i] + b62 * k2[i] + b63 * k3[i] + b64 * k4[i] + b65 * k5[i]);
k6[i] = h * s[i].getRate();
}
for (int i = 0; i < numberOfSubstances; i++) {
y2[i] = y1[i] + c1 * k1[i] + c3 * k3[i] + c4 * k4[i] + c6 * k6[i]; // fifth
// order
// estimate
//
// error between 4th and 5th
//
// note that the errors are scaled with respect to estimated new
// values
// if the new values are smaller than 1e-8, scale to 1e-8. This
// number is
// used to avoid scaling with respect to a number that is too small.
//
yerr[i] =
Math.abs(
(dc1 * k1[i] + dc3 * k3[i] + dc4 * k4[i] + dc5 * k5[i] + dc6 * k6[i])
/ Math.max(Math.abs(y2[i]), 1e-8));
}
}
