protected SingleOdeEngine(Func <double, double, double> rhs, double x, OdeEvaluationSettings settings) : base(x)
{
Debug.Assert(rhs != null);
Debug.Assert(settings != null);
this.rhs = rhs;
this.settings = settings;
}
public SingleBulrischStoerEngine(Func <double, double, double> rhs, double x, double y, OdeEvaluationSettings settings) : base(rhs, x, settings)
{
this.Y = y;
this.YPrime = this.Evaluate(x, y);
ComputeInitialStep();
}
/// <summary>
/// Solves a conservative second order ordinary differential equation initial value problem using the given settings.
/// </summary>
/// <param name="rhs">The right hand side function.</param>
/// <param name="x0">The initial value of the independent variable.</param>
/// <param name="y0">The initial value of the function variable.</param>
/// <param name="yPrime0">The intial value of the function derivative.</param>
/// <param name="x1">The final value of the independent variable.</param>
/// <param name="settings">The settings to use when solving the problem.</param>
/// <returns>The solution, including the final value of the function and its derivative.</returns>
/// <exception cref="ArgumentNullException">The <paramref name="rhs"/> or <paramref name="settings"/> is null.</exception>
/// <exception cref="NonconvergenceException">The ODE could not be integrated to the required precision before exhausting the maximum allowed number of <paramref name="rhs"/> evaluations.</exception>
/// <remarks>
/// <para>A conservative ODE is an ODE of the form</para>
/// <img src="../images/ConservativeODE.png" />
/// <para>where the right-hand-side depends only on x and y, not on the derivative y'. ODEs of this form are called conservative because
/// they exhibit conserved quantities: combinations of y and y' that maintain the same value as the system evolves. Many forms of
/// Newtonian equations of motion, for example, are conservative ODEs, with conserved quantities such as energy, momentum, and
/// angular momentum. Our specialized conservative ODE integrator is not only more efficient for conservative ODEs, but does a
/// better job of maintaining the conserved quantities.</para>
/// </remarks>
public static OdeResult IntegrateConservativeOde(Func <double, double, double> rhs, double x0, double y0, double yPrime0, double x1, OdeEvaluationSettings settings)
{
if (rhs == null)
{
throw new ArgumentNullException(nameof(rhs));
}
if (settings == null)
{
throw new ArgumentNullException(nameof(settings));
}
SetOdeDefaults(settings);
SingleStoermerEngine engine = new SingleStoermerEngine(rhs, x0, y0, yPrime0, settings);
BulrischStoerStrategy strategy = new BulrischStoerStrategy(engine);
strategy.IntegrateTo(x1);
return(engine.GetResult());
}
