Packages

o

scalation.dynamics

RungeKutta

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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  1. final def !=(arg0: Any): Boolean
    Definition Classes
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  2. final def ##(): Int
    Definition Classes
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  3. final def ==(arg0: Any): Boolean
    Definition Classes
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  4. final def asInstanceOf[T0]: T0
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  5. def clone(): AnyRef
    Attributes
    protected[java.lang]
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    @native() @throws( ... )
  6. val defaultStepSize: Double

    The default step size for the t dimension

    The default step size for the t dimension

    Attributes
    protected
    Definition Classes
    Integrator
  7. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  8. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  9. val error: Double

    Estimate of the error in calculating y

    Estimate of the error in calculating y

    Attributes
    protected
    Definition Classes
    Integrator
  10. def finalize(): Unit
    Attributes
    protected[java.lang]
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    @throws( classOf[java.lang.Throwable] )
  11. final def flaw(method: String, message: String): Unit
    Definition Classes
    Error
  12. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  13. def getError: Double

    Get the error estimate.

    Get the error estimate.

    Definition Classes
    Integrator
  14. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  15. 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

    Definition Classes
    RungeKutta → Integrator
  16. 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

    Definition Classes
    Integrator
  17. 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

    Definition Classes
    RungeKutta → Integrator
  18. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  19. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  20. final def notify(): Unit
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    AnyRef
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    @native()
  21. final def notifyAll(): Unit
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  22. final def synchronized[T0](arg0: ⇒ T0): T0
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  23. def toString(): String
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  24. final def wait(): Unit
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    @throws( ... )
  25. final def wait(arg0: Long, arg1: Int): Unit
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    @throws( ... )
  26. final def wait(arg0: Long): Unit
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Inherited from Integrator

Inherited from Error

Inherited from AnyRef

Inherited from Any

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