Packages

o

scalation.dynamics

DormandPrince

object DormandPrince extends Integrator

The DormandPrince object provides a state-of-the-art 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 (4,5)-order Dormand-Prince Integrator 'DOPRI'. Note: the 'integrateV' method for a system of separable ODEs is mixed in from the Integrator trait.

See also

http://adorio-research.org/wordpress/?p=6565

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Integrator, Error, AnyRef, Any
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  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. val a21: Double

    Butcher tableau @see http://en.wikipedia.org/wiki/Dormand–Prince_method

  5. val a31: Double
  6. val a32: Double
  7. val a41: Double
  8. val a42: Double
  9. val a43: Double
  10. val a51: Double
  11. val a52: Double
  12. val a53: Double
  13. val a54: Double
  14. val a61: Double
  15. val a62: Double
  16. val a63: Double
  17. val a64: Double
  18. val a65: Double
  19. val a71: Double
  20. val a72: Double
  21. val a73: Double
  22. val a74: Double
  23. val a75: Double
  24. val a76: Double
  25. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  26. val b1: Double
  27. val b1p: Double
  28. val b2: Double
  29. val b2p: Double
  30. val b3: Double
  31. val b3p: Double
  32. val b4: Double
  33. val b4p: Double
  34. val b5: Double
  35. val b5p: Double
  36. val b6: Double
  37. val b6p: Double
  38. val b7: Double
  39. val b7p: Double
  40. val c2: Double
  41. val c3: Double
  42. val c4: Double
  43. val c5: Double
  44. val c6: Double
  45. val c7: Double
  46. def clone(): AnyRef
    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  47. val defaultStepSize: Double

    The default step size for the t dimension

    The default step size for the t dimension

    Attributes
    protected
    Definition Classes
    Integrator
  48. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  49. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  50. val error: Double

    Estimate of the error in calculating y

    Estimate of the error in calculating y

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

    Get the error estimate.

    Get the error estimate.

    Definition Classes
    Integrator
  55. def hashCode(): Int
    Definition Classes
    AnyRef → Any
  56. 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 (4,5)-order Dormand-Prince 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 (4,5)-order Dormand-Prince method to return the value of y(t) at time t.

    f

    the derivative function f(t, y)

    y0

    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 middle step size

    Definition Classes
    DormandPrince → Integrator
  57. def integrate2(f: Derivative, y0: Double, t: Double, hmin: Double, hmax: Double, t0: Double = 0.0, tol: Double = 1E-5, maxSteps: Int = 1000): Double

    Compute y(t) governed by a differential equation using numerical integration of the derivative function f(t, y) using a (4,5)-order Dormand-Prince 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 (4,5)-order Dormand-Prince method to return the value of y(t) at time t. The method provides more customization options.

    f

    the derivative function f(t, y)

    y0

    value of the y-function at time t0, y0 = y(t0)

    t

    the time value at which to compute y(t)

    hmin

    the minimum step size

    hmax

    the maximum step size

    t0

    the initial time

    tol

    the tolerance

    maxSteps

    the maximum number of steps

  58. 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
  59. 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 (4,5)-order Dormand-Prince 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 (4,5)-order Dormand-Prince 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
    DormandPrince → Integrator
  60. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  61. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  62. final def notify(): Unit
    Definition Classes
    AnyRef
  63. final def notifyAll(): Unit
    Definition Classes
    AnyRef
  64. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  65. def toString(): String
    Definition Classes
    AnyRef → Any
  66. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  67. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  68. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Integrator

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