scalation.dynamics

DormandPrince

Related Doc: package dynamics

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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  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

    Definition Classes
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  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. var 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]
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    @throws( classOf[java.lang.Throwable] )

  52. def flaw(method: String, message: String): Unit

    Show the flaw by printing the error message.

    Show the flaw by printing the error message.

    method

    the method where the error occurred

    message

    the error message

    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

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  64. final def synchronized[T0](arg0: ⇒ T0): T0

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  65. def toString(): String

    Definition Classes
    AnyRef → Any

  66. final def wait(): Unit

    Definition Classes
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    @throws( ... )

  67. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
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    @throws( ... )

  68. final def wait(arg0: Long): Unit

    Definition Classes
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    @throws( ... )

Inherited from Integrator

Inherited from Error

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