public override ODEState Solve(IODEEquation eq, ODEState initialState, double time, double timeStep)
{
ODEState deriv = eq.GetDerivative(time, initialState);
// Compute new state using Euler's method
// Yn+1 = Yn + deltaT * dYn/dt
return(initialState.AddScaled(deriv, timeStep));
}
public override ODEState Solve(IODEEquation eq, ODEState initialState, double time, double timeStep)
{
ODEState k1 = eq.GetDerivative(time, initialState);
ODEState k2 = eq.GetDerivative(time + timeStep / 2, initialState.AddScaled(k1, timeStep / 2));
ODEState k3 = eq.GetDerivative(time + timeStep / 2, initialState.AddScaled(k2, timeStep / 2));
ODEState k4 = eq.GetDerivative(time + timeStep, initialState.AddScaled(k3, timeStep));
ODEState sum = k1.AddScaled(k2, 2).AddScaled(k3, 2).AddScaled(k4, 1);
return(initialState.AddScaled(sum, timeStep / 6));
}
/// <summary>
/// This method solves the ODE from the initial time to the final time
/// by dividing this interval into timesteps and calling the other
/// solve method for each time step.
/// </summary>
/// <param name="eq"> The ODE to solve </param>
/// <param name="initialState"> Initial state of the ODE </param>
/// <param name="initialTime"> Time at which to start </param>
/// <param name="finalTime"> Time at which to stop </param>
/// <param name="timeStep"> Hint of the time step to use </param>
/// <returns> The state of the ODE at finalTime </returns>
public virtual ODEState Solve(IODEEquation eq, ODEState initialState, double initialTime, double finalTime, double timeStep)
{
double t;
ODEState y = initialState;
for (t = initialTime; t < finalTime; t += timeStep)
{
y = Solve(eq, y, t, timeStep);
}
if (t < finalTime)
{
y = Solve(eq, y, t, finalTime - t);
}
return(y);
}
public abstract ODEState Solve(IODEEquation eq, ODEState initialState, double time, double timeStep);
