object RungeKutta extends Integrator
The RungeKutta object provides an implementation of a classical numerical
ODE solver. Given an unknown, time-dependent function 'y(t)' governed by an
Ordinary Differential Equation (ODE) of the form:
d/dt y(t) = f(t, y)
Compute 'y(t)' using a 4th-order Runge-Kutta Integrator 'RK4'. Note: the
'integrateV' method for a system of separable ODEs is mixed in from the
Integrator trait.
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- val defaultStepSize: Double
The default step size for the t dimension
The default step size for the t dimension
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- val error: Double
Estimate of the error in calculating y
Estimate of the error in calculating y
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- def getError: Double
Get the error estimate.
Get the error estimate.
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- def integrate(f: Derivative, y0: Double, t: Double, t0: Double = 0.0, step: Double = defaultStepSize): Double
Compute y(t) governed by a differential equation using numerical integration of the derivative function f(t, y) using a 4th-order Runge-Kutta method to return the value of y(t) at time t.
Compute y(t) governed by a differential equation using numerical integration of the derivative function f(t, y) using a 4th-order Runge-Kutta method to return the value of y(t) at time t.
- f
the derivative function f(t, y) where y is a scalar
- y0
the value of the y-function at time t0, y0 = y(t0)
- t
the time value at which to compute y(t)
- t0
the initial time
- step
the step size
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- RungeKutta → Integrator
- def integrateV(f: Array[Derivative], y0: VectorD, t: Double, t0: Double = 0.0, step: Double = defaultStepSize): VectorD
Apply the integrate method to each derivative to compute the trajectory of a time-dependent vector function y(t) governed by a separable system of Ordinary Differential Equations (ODE's) where [f_j(t, y_j)] is an array of derivative functions.
Apply the integrate method to each derivative to compute the trajectory of a time-dependent vector function y(t) governed by a separable system of Ordinary Differential Equations (ODE's) where [f_j(t, y_j)] is an array of derivative functions. Each derivative function takes a scalar t and a scalar y_j = y(j).
- f
the array of derivative functions [f_j(t, y_j)]
- y0
the initial value vector, y0 = y(t0)
- t
the time value at which to compute y(t)
- t0
the initial time
- step
the step size
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- def integrateVV(f: Array[DerivativeV], y0: VectorD, t: Double, t0: Double = 0.0, step: Double = defaultStepSize): VectorD
Compute y(t), a vector, governed by a system of differential equations using numerical integration of the derivative function f(t, y) using a 4th-order Runge-Kutta method to return the value of y(t) at time t.
Compute y(t), a vector, governed by a system of differential equations using numerical integration of the derivative function f(t, y) using a 4th-order Runge-Kutta method to return the value of y(t) at time t.
- f
the array of derivative functions [f(t, y)] where y is a vector
- y0
the value of the y-function at time t0, y0 = y(t0)
- t
the time value at which to compute y(t)
- t0
the initial time
- step
the step size
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