public static double[] embedded_estimate(
double h,
double[] xold,
double[] xnew,
double[] xe,
double[] atol,
double[] rtol,
double p,
double aMax,
double aMin,
double alpha) {
// initializations
int n = xold.length;
double[] tau = new double[n];
double[] ad1 = new double[n];
double[] dq1 = new double[n];
double hOpt;
double epsilon;
double hNew;
// calculations
StdMet.tau(tau, xold, xnew, atol, rtol); // get the array of
// tolerances for this step
StdMet.arraydiff(ad1, xnew, xe); // (higer order solution - lower order solution)
StdMet.dotQuo(dq1, ad1, tau); // ad1/tau
epsilon = StdMet.rmsNorm(dq1); // epsilon = rmsNorm(ad1/tau)
// calculate h and see if it is optimal
hOpt = h * Math.pow((1.0 / epsilon), 1.0 / p); // calculate
// optimal stepsize for next step
hNew = Math.min(aMax * h, Math.max(aMin * h, alpha * hOpt));
// calculate hNew with h and hOpt
double[] estimation = new double[2];
estimation[0] = epsilon;
estimation[1] = hNew;
return (estimation);
}
public static double[] stepdoubling_estimate(
double h,
double[] eta1,
double[] eta2,
double[] xtemp,
double atol,
double rtol,
double p,
double amax,
double alpha) {
// initializations
int n = eta1.length;
double[] diff1 = new double[n];
double[] err = new double[n];
double[] eps = new double[n];
double[] est = new double[n];
double norm;
double hopt;
double hNew;
// calculations
StdMet.arraydiff(diff1, eta2, eta1); // get error
StdMet.stam(err, 1 / (Math.pow(2, p) - 1), diff1);
StdMet.epsilon(eps, xtemp, eta1, atol, rtol); // get epsilon
StdMet.dotQuo(est, err, eps);
norm = StdMet.rmsNorm(est); // take norm of est
// calculate h and see if it is optimal
hopt = h / (Math.pow(Math.pow(2, p) * StdMet.rmsNorm(est), (1 / (p + 1))));
hNew = Math.min(amax * h, Math.max((1 / amax) * h, alpha * 2 * hopt));
// calculate hNew with h and hOpt
double[] estimation = new double[3];
estimation[0] = hNew;
estimation[1] = hopt;
estimation[2] = norm;
return (estimation);
}