public void OdeSine()
{
// The sine and cosine functions satisfy
// y'' = - y
// This is perhaps the simplest conservative differential equation.
// (i.e. right hand side depends only on y, not y')
Func <double, double, double> f = (double x, double y) => - y;
int count = 0;
OdeSettings settings = new OdeSettings()
{
Listener = (OdeResult r) => {
Assert.IsTrue(TestUtilities.IsNearlyEqual(
MoreMath.Sqr(r.Y) + MoreMath.Sqr(r.YPrime), 1.0, r.Settings
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
r.Y, MoreMath.Sin(r.X), r.Settings
));
count++;
}
};
OdeResult result = FunctionMath.IntegrateConservativeOde(f, 0.0, 0.0, 1.0, 5.0, settings);
Assert.IsTrue(TestUtilities.IsNearlyEqual(result.Y, MoreMath.Sin(5.0)));
Assert.IsTrue(count > 0);
}
public static void IntegrateOde()
{
Func <double, double, double> rhs = (x, y) => - x * y;
OdeResult sln = FunctionMath.IntegrateOde(rhs, 0.0, 1.0, 2.0);
Console.WriteLine($"Numeric solution y({sln.X}) = {sln.Y}.");
Console.WriteLine($"Required {sln.EvaluationCount} evaluations.");
Console.WriteLine($"Analytic solution y({sln.X}) = {Math.Exp(-MoreMath.Sqr(sln.X) / 2.0)}");
// Lotka-Volterra equations
double A = 0.1;
double B = 0.02;
double C = 0.4;
double D = 0.02;
Func <double, IReadOnlyList <double>, IReadOnlyList <double> > lkRhs = (t, y) => {
return(new double[] {
A *y[0] - B * y[0] * y[1], D *y[0] * y[1] - C * y[1]
});
};
MultiOdeSettings lkSettings = new MultiOdeSettings()
{
Listener = r => { Console.WriteLine($"t={r.X} rabbits={r.Y[0]}, foxes={r.Y[1]}"); }
};
MultiFunctionMath.IntegrateOde(lkRhs, 0.0, new double[] { 20.0, 10.0 }, 50.0, lkSettings);
Func <double, IReadOnlyList <double>, IReadOnlyList <double> > rhs1 = (x, u) => {
return(new double[] { u[1], -u[0] });
};
MultiOdeSettings settings1 = new MultiOdeSettings()
{
EvaluationBudget = 100000
};
MultiOdeResult result1 = MultiFunctionMath.IntegrateOde(
rhs1, 0.0, new double[] { 0.0, 1.0 }, 500.0, settings1
);
double s1 = MoreMath.Sqr(result1.Y[0]) + MoreMath.Sqr(result1.Y[1]);
Console.WriteLine($"y({result1.X}) = {result1.Y[0]}, (y)^2 + (y')^2 = {s1}");
Console.WriteLine($"Required {result1.EvaluationCount} evaluations.");
Func <double, double, double> rhs2 = (x, y) => - y;
OdeSettings settings2 = new OdeSettings()
{
EvaluationBudget = 100000
};
OdeResult result2 = FunctionMath.IntegrateConservativeOde(
rhs2, 0.0, 0.0, 1.0, 500.0, settings2
);
double s2 = MoreMath.Sqr(result2.Y) + MoreMath.Sqr(result2.YPrime);
Console.WriteLine($"y({result2.X}) = {result2.Y}, (y)^2 + (y')^2 = {s2}");
Console.WriteLine($"Required {result2.EvaluationCount} evaluations");
Console.WriteLine(MoreMath.Sin(500.0));
}
public void OdeNonlinear()
{
// y = \frac{y_0}{1 - y_0 (x - x_0)}
Func <double, double, double> f = (double x, double y) => MoreMath.Sqr(y);
int count = 0;
OdeSettings settings = new OdeSettings()
{
RelativePrecision = 1.0E-8,
EvaluationBudget = 1024,
Listener = (OdeResult) => count++
};
OdeResult result = FunctionMath.IntegrateOde(f, 0.0, 1.0, 0.99, settings);
Assert.IsTrue(TestUtilities.IsNearlyEqual(result.Y, 1.0 / (1.0 - 1.0 * (0.99 - 0.0)), result.Settings));
Assert.IsTrue(count > 0);
Console.WriteLine(result.EvaluationCount);
}
