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;
OdeEvaluationSettings settings = new OdeEvaluationSettings()
{
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);
}
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;
OdeEvaluationSettings settings = new OdeEvaluationSettings()
{
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
));
}
};
OdeResult result = FunctionMath.IntegrateConservativeOde(f, 0.0, 0.0, 1.0, 5.0, settings);
Assert.IsTrue(TestUtilities.IsNearlyEqual(result.Y, MoreMath.Sin(5.0)));
Console.WriteLine(result.EvaluationCount);
}