/// <summary>
/// Solves an ODE using RK2
/// </summary>
/// <param name="initial"></param>
/// <param name="x"></param>
/// <param name="h"></param>
/// <param name="system"></param>
/// <returns></returns>
private static float[] SolveRK2(float[] initial, float x, float h, CalculateDerivativesHandler calculateDerivatives)
{
// do Euler step with half the step value
float[] k1 = calculateDerivatives(initial, x);
float[] temp = DoEulerStep(initial, k1, h / 2.0f);
// calculate again at midpoint
float[] k2 = calculateDerivatives(temp, x + (h / 2.0f));
// use derivatives for complete timestep
return DoEulerStep(initial, k2, h);
}
/// <summary>
/// This method solves first-order ODEs. It is passed an array
/// of dependent variables in "array" at x, and returns an
/// array of new values at x + h.
/// </summary>
/// <param name="initial">Array of initial values</param>
/// <param name="x">Initial value of x (usually time)</param>
/// <param name="h">Increment value for x (usually delta time)</param>
/// <param name="system">Class containing a method to calculate the
/// derivatives of the initial values</param>
/// <param name="integrator">Type of numeric
/// integration to use</param>
/// <returns></returns>
public static float[] Solve(float[] initial, float x, float h,
CalculateDerivativesHandler calculateDerivatives,
Integrator integrator)
{
switch (integrator)
{
case Integrator.Euler :
return SolveEuler(initial, x, h, calculateDerivatives);
case Integrator.RK2 :
return SolveRK2(initial, x, h, calculateDerivatives);
case Integrator.RK4 :
goto default;
default :
return SolveRK4(initial, x, h, calculateDerivatives);
}
}
/// <summary>
/// Solves an ODE using Euler integration
/// </summary>
/// <param name="initial"></param>
/// <param name="x"></param>
/// <param name="h"></param>
/// <param name="system"></param>
/// <returns></returns>
private static float[] SolveEuler(float[] initial, float x, float h, CalculateDerivativesHandler calculateDerivatives)
{
// final = initial + derived * h
float[] derivs = calculateDerivatives(initial, x);
return DoEulerStep(initial, derivs, h);
}
/// <summary>
/// Solves an ODE using RK4
/// </summary>
/// <param name="initial"></param>
/// <param name="x"></param>
/// <param name="h"></param>
/// <param name="system"></param>
/// <returns></returns>
private static float[] SolveRK4(float[] initial, float x, float h, CalculateDerivativesHandler calculateDerivatives)
{
float[] k1 = calculateDerivatives(initial, x);
float[] temp = DoEulerStep(initial, k1, h / 2.0f);
float[] k2 = calculateDerivatives(temp, x + (h / 2.0f));
temp = DoEulerStep(initial, k2, h / 2.0f);
float[] k3 = calculateDerivatives(temp, x + (h / 2.0f));
temp = DoEulerStep(initial, k3, h);
float[] k4 = calculateDerivatives(temp, x + h);
float[] ret = DoEulerStep(initial, k1, h / 6.0f);
ret = DoEulerStep(ret, k2, h / 3.0f);
ret = DoEulerStep(ret, k3, h / 3.0f);
ret = DoEulerStep(ret, k4, h / 6.0f);
return ret;
}
