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.

Linear Supertypes
Integrator, Error, AnyRef, Any
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. RungeKutta
  2. Integrator
  3. Error
  4. AnyRef
  5. Any
  1. Hide All
  2. Show All
Visibility
  1. Public
  2. All

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @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]
    Definition Classes
    AnyRef
    Annotations
    @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
  13. def getError: Double

    Get the error estimate.

    Get the error estimate.

    Definition Classes
    Integrator
  14. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  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
    Definition Classes
    AnyRef
  21. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  22. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  23. def toString(): String
    Definition Classes
    AnyRef → Any
  24. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  25. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  26. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Integrator

Inherited from Error

Inherited from AnyRef

Inherited from Any

Ungrouped