public void OdeExponential()
{
// Exponential
// y = y_0 e^{x - x_0}
Func <double, double, double> f = (double x, double y) => y;
double y1 = FunctionMath.SolveOde(f, 0.0, 1.0, 2.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(y1, MoreMath.Sqr(Math.E)));
}
public void OdeExample()
{
Func <double, double, double> rhs = (double t, double u) => (1.0 - 2.0 * t) * u;
Func <double, double, double> solution = (double u0, double t) => u0 *Math.Exp(t - t *t);
foreach (double t in new double[] { 0.5, 0.75, 1.50, 2.25, 3.25 })
{
double y1 = FunctionMath.SolveOde(rhs, 0.0, 1.0, t);
Assert.IsTrue(TestUtilities.IsNearlyEqual(y1, solution(1.0, t)));
}
}
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);
EvaluationSettings settings = new EvaluationSettings()
{
RelativePrecision = 1.0E-8, EvaluationBudget = 1000
};
double y1 = FunctionMath.SolveOde(f, 0.0, 1.0, 0.99, settings);
Console.WriteLine(y1);
Assert.IsTrue(TestUtilities.IsNearlyEqual(y1, 1.0 / (1.0 - 1.0 * (0.99 - 0.0)), settings));
}
public void OdeLogistic()
{
// y = \frac{y_0}{y_0 + (1 - y_0) e^{-(x - x_0)}
Func <double, double, double> rhs = (double x, double y) => y * (1.0 - y);
Func <double, double, double> solution = (double y0, double x) => y0 / (y0 + (1.0 - y0) * Math.Exp(-x));
foreach (double y0 in new double[] { -0.1, 0.0, 0.4, 1.0, 1.6 })
{
Console.WriteLine(y0);
Interval r = Interval.FromEndpoints(0.0, 2.0);
double y1 = FunctionMath.SolveOde(rhs, 0.0, y0, 2.0);
Console.WriteLine(y1);
Assert.IsTrue(TestUtilities.IsNearlyEqual(y1, solution(y0, 2.0)));
}
}