RK |
Runge-Kutta method of 5th order of Dormand and Prince with 6 stages.
Attention: This method can only provide dense output of order 3.
If dense output of high accuracy is needed, use method RK547M .
Inheritance HierarchyNamespace: Altaxo.Calc.Ode
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
public class RK546M : RungeKuttaExplicitBase
The RK546M type exposes the following members.
ConstructorsProperties| Name | Description | |
|---|---|---|
 | A | Central coefficients of the Runge-Kutta scheme. See [1], page 135. (Overrides RungeKuttaExplicitBaseA) |
| A_Interpolation |
Gets additional central coefficients of the Runge-Kutta scheme that are used for dense output (interpolation).
(Inherited from RungeKuttaExplicitBase) |
 | AbsoluteTolerance |
Gets or sets the absolute tolerance.
(Inherited from RungeKuttaExplicitBase) |
| AbsoluteTolerances |
Gets or sets the absolute tolerances. The length of the array must either be 1 (tolerances for all y equal), or of length N.
(Inherited from RungeKuttaExplicitBase) |
| BH | High order bottom side coefficients of the Runge-Kutta scheme. (Overrides RungeKuttaExplicitBaseBH) |
| BHML | Differences between high order and low order bottom side coefficients of the Runge-Kutta scheme. (Overrides RungeKuttaExplicitBaseBHML) |
| C | Left side coefficients of the Runge-Kutta scheme. (Overrides RungeKuttaExplicitBaseC) |
| C_Interpolation |
Gets additional left side coefficients of the Runge-Kutta scheme (x-partitions) that are used for dense output (interpolation).
(Inherited from RungeKuttaExplicitBase) |
| InterpolationCoefficients |
The interpolation coefficients aij. Note that zero to third order interpolation is using y and slope of x_previous and x_current.
Thus in this array we only need the coefficients for 4th order (and higher) interpolation.
(Inherited from RungeKuttaExplicitBase) |
| NewCoreNotInitializedException |
Creates a new exception that indicates that the core is not initialized.
(Inherited from RungeKuttaExplicitBase) |
| NumberOfAdditionalStagesForDenseOutput |
Gets the number of stages of additional stages needed for dense output.
(Inherited from RungeKuttaExplicitBase) |
| NumberOfStages |
Gets the number of stages for the main process (stages needed for dense output not included).
(Overrides RungeKuttaExplicitBaseNumberOfStages) |
| Order |
Gets the order of the method (the highest of the pair).
(Overrides RungeKuttaExplicitBaseOrder) |
| RelativeTolerance |
Gets or sets the relative tolerance.
(Inherited from RungeKuttaExplicitBase) |
| RelativeTolerances |
Gets or sets the relative tolerances. The length of the array must either be 1 (tolerances for all y equal), or of length N.
(Inherited from RungeKuttaExplicitBase) |
| StiffnessDetectionEveryNumberOfSteps |
Gets or sets the number of successful steps between test for stiffness.
Setting this value to 0 disables stiffness detection. The default value is 0.
(Inherited from RungeKuttaExplicitBase) |
| StiffnessDetectionThresholdValue |
Sets the stiffness detection threshold value.
(Overrides RungeKuttaExplicitBaseStiffnessDetectionThresholdValue) |
Methods| Name | Description | |
|---|---|---|
 | EnumerateXForFixedStepSize |
Enumerates the endless sequence x_current + k * stepSize, for k=1..Infinity.
(Inherited from RungeKuttaExplicitBase) |
 | Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
| Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetInitialStepSize |
Gets the initial step size. The absolute and relative tolerances must be set before the call to this function.
(Inherited from RungeKuttaExplicitBase) |
| GetInterpolatedSolutionPointVolatile |
Gets you an interpolated volative solution point during the enumeration of the solution points.
The returned array must not be modified and has to be immediately consumed, since it is changed in the course of the next ODE evaluation.
(Inherited from RungeKuttaExplicitBase) |
| GetSolutionPoints |
Gets a sequence of solution points, using the settings in the argument.
(Inherited from RungeKuttaExplicitBase) |
| GetSolutionPointsForStepSize(Double) |
Gets solution points for constant step size. Returns the same results as GetSolutionPointsVolatileForStepSize(Double, Double, ActionDouble, Double, Double, Double),
but the returned solution point already contains a copy of the y array.
(Inherited from RungeKuttaExplicitBase) |
| GetSolutionPointsForStepSize(Double, Double, ActionDouble, Double, Double, Double) |
Gets solution points for constant step size. Returns the same results as GetSolutionPointsVolatileForStepSize(Double, Double, ActionDouble, Double, Double, Double),
but the returned solution point already contains a copy of the y array.
(Inherited from RungeKuttaExplicitBase) |
| GetSolutionPointsVolatile |
Gets a sequence of solution points, using the settings in the argument. The y-values in the returned tuple
are intended for immediate consumption, because the content of the array will change in the further course of the
evaluation.
(Inherited from RungeKuttaExplicitBase) |
| GetSolutionPointsVolatile_WithoutStepSizeControl |
Gets volatile solution points without step size control.
(Inherited from RungeKuttaExplicitBase) |
| GetSolutionPointsVolatile_WithStepSizeControl |
Gets volatile solution points with step size control.
(Inherited from RungeKuttaExplicitBase) |
| GetSolutionPointsVolatileForStepSize(Double) |
Gets volatile solution points for constant step size. The method has to be initialized (see Initialize(Double, Double, ActionDouble, Double, Double)) before.
(Inherited from RungeKuttaExplicitBase) |
| GetSolutionPointsVolatileForStepSize(Double, Double, ActionDouble, Double, Double, Double) |
Initializes the method and gets volatile solution points for constant step size.
(Inherited from RungeKuttaExplicitBase) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| Initialize |
Initializes the Runge-Kutta method.
(Inherited from RungeKuttaExplicitBase) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| SetOptionsToCore |
Provides the core with the parameters found in the options.
(Inherited from RungeKuttaExplicitBase) |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
| TryGetNextValue |
Try to get the smaller value of the two enumerations. After that, the enumeration with the smaller value is advanced by one step.
(Inherited from RungeKuttaExplicitBase) |
Fields| Name | Description | |
|---|---|---|
 | _core |
The solver core.
(Inherited from RungeKuttaExplicitBase) |
RemarksReferences:
[1] Hairer, Ordinary differential equations I, 2nd edition, 1993.
[2] Jimenez et al., Locally Linearized Runge Kutta method of Dormand and Prince, arXiv:1209.1415v2, 22 Dec 2013
[3] Engeln-Müllges et al., Numerik-Algorithmen, Springer, 2011 (in German)
See Also