public void OdeLRC()
{
double L = 1.0;
double R = 1.0;
double C = 1.0;
Func <double, IList <double>, IList <double> > rhs = (double x, IList <double> y) => {
double q = y[0]; double qp = y[1];
return(new double[] {
qp,
(0.0 - q / C - R * qp) / L
});
};
double q0 = 1.0;
double qp0 = 0.0;
double t0 = 2.0 * L / R;
double w0 = Math.Sqrt(1.0 / (L * C) - 1.0 / (t0 * t0));
double t = 1.0;
double sc = (q0 * Math.Cos(w0 * t) + (qp0 + q0 / t0) / w0 * Math.Sin(w0 * t)) * Math.Exp(-t / t0);
Console.WriteLine(sc);
IList <double> s = MultiFunctionMath.SolveOde(rhs, 0.0, new double[] { q0, qp0 }, t).Y;
Console.WriteLine(s[0]);
}
public void OdeLorenz()
{
double sigma = 10.0;
double beta = 8.0 / 3.0;
double rho = 28.0;
Func <double, IList <double>, IList <double> > rhs = (double t, IList <double> u) => new ColumnVector(
sigma * (u[1] - u[0]),
u[0] * (rho - u[2]) - u[1],
u[0] * u[1] - beta * u[2]
);
ColumnVector u0 = new ColumnVector(1.0, 1.0, 1.0);
MultiFunctionMath.SolveOde(rhs, 0.0, u0, 10.0, new EvaluationSettings()
{
RelativePrecision = 1.0E-8, EvaluationBudget = 100000
});
}
public void OdeEuler()
{
// Euler's equations for rigid body motion (without external forces) are
// I_1 \dot{\omega}_1 = (I_2 - I_3) \omega_2 \omega_3
// I_2 \dot{\omega}_2 = (I_3 - I_1) \omega_3 \omega_1
// I_3 \dot{\omega}_3 = (I_1 - I_2) \omega_1 \omega_2
// where \omega's are rotations about the principal axes and I's are the moments
// of inertia about those axes. The rotational kinetic energy
// I_1 \omega_1^2 + I_2 \omega_2^2 + I_3 \omega_3^2 = 2E
// and angular momentum
// I_1^2 \omega_1^2 + I_2^2 \omega_2^2 + I_3^2 \omega_3^2 = M^2
// are conserved quantities.
ColumnVector I = new ColumnVector(1.0, 2.0, 3.0);
Func <double, IList <double>, IList <double> > rhs = (double t, IList <double> w) => {
return(new ColumnVector((I[1] - I[2]) * w[1] * w[2] / I[0], (I[2] - I[0]) * w[2] * w[0] / I[1], (I[0] - I[1]) * w[0] * w[1] / I[2]));
};
ColumnVector w0 = new ColumnVector(1.0, 1.0, 1.0);
double eps = 1.0E-12;
EvaluationSettings settings = new EvaluationSettings()
{
RelativePrecision = eps,
AbsolutePrecision = eps * eps,
EvaluationBudget = 10000
};
settings.UpdateHandler = (EvaluationResult r) => {
OdeResult <IList <double> > q = (OdeResult <IList <double> >)r;
Console.WriteLine("{0} {1}", q.EvaluationCount, q.X);
Assert.IsTrue(TestUtilities.IsNearlyEqual(EulerKineticEnergy(I, q.Y), EulerKineticEnergy(I, w0), settings));
Assert.IsTrue(TestUtilities.IsNearlyEqual(EulerAngularMomentum(I, q.Y), EulerAngularMomentum(I, w0), settings));
};
MultiFunctionMath.SolveOde(rhs, 0.0, w0, 10.0, settings);
}
public void OdeOrbit2()
{
Func <double, IList <double>, IList <double> > rhs = (double t, IList <double> r) => {
double d = MoreMath.Hypot(r[0], r[2]);
double d3 = MoreMath.Pow(d, 3);
return(new ColumnVector(r[1], -r[0] / d3, r[3], -r[2] / d3));
};
//double e = 0.5;
foreach (double e in TestUtilities.GenerateUniformRealValues(0.0, 1.0, 8))
{
Console.WriteLine(e);
ColumnVector r0 = new ColumnVector(1.0 - e, 0.0, 0.0, Math.Sqrt((1.0 + e) / (1.0 - e)));
ColumnVector r1 = new ColumnVector(MultiFunctionMath.SolveOde(rhs, 0.0, r0, 2.0 * Math.PI).Y);
Assert.IsTrue(TestUtilities.IsNearlyEqual(r0, r1, new EvaluationSettings()
{
RelativePrecision = 1.0E-9
}));
}
}
