STK Components for .NET 2022 r2

## RungeKuttaVerner89Integrator Class |

This is an eighth order Runge-Kutta algorithm with error control based on the work
of Verner which can adapt the size of the integration step based on comparing the
ninth order evaluation with the eighth order evaluation to produce an estimate of
the numerical error produced by a given integration step.

Inheritance Hierarchy

SystemObject

AGI.Foundation.NumericalMethodsNumericalIntegrator

AGI.Foundation.NumericalMethods.AdvancedAdaptiveNumericalIntegrator

AGI.Foundation.NumericalMethods.AdvancedRungeKuttaAdaptiveStepIntegrator

AGI.Foundation.NumericalMethodsRungeKuttaVerner89Integrator

AGI.Foundation.NumericalMethodsNumericalIntegrator

AGI.Foundation.NumericalMethods.AdvancedAdaptiveNumericalIntegrator

AGI.Foundation.NumericalMethods.AdvancedRungeKuttaAdaptiveStepIntegrator

AGI.Foundation.NumericalMethodsRungeKuttaVerner89Integrator

Syntax

The RungeKuttaVerner89Integrator type exposes the following members.

Constructors

Name | Description | |
---|---|---|

RungeKuttaVerner89Integrator | Initializes a new instance. | |

RungeKuttaVerner89Integrator(DependentVariableDerivatives, Double) |
Initializes a new instance based on the given system of equations and initial step size.
| |

RungeKuttaVerner89Integrator(RungeKuttaVerner89Integrator, CopyContext) | Initializes a new instance as a copy of an existing instance. |

Properties

Name | Description | |
---|---|---|

AbsoluteTolerance |
Gets or sets the tolerance which provides a baseline for the error control.
By default, this value is Epsilon10.
| |

AdaptiveWeights |
Gets or sets the weights to be applied to the state elements when
computing the error which determines how to adapt the step size.
This is in addition to any weights used in the integration algorithm
itself. If these weights have not been initialized before
Initialize(Double, Double) is called, they will be set to a default value
of one.
(Inherited from AdaptiveNumericalIntegrator.) | |

CurrentStepSize |
Gets the current (positive) size of the step which the integrator will use for the next integration step.
(Inherited from AdaptiveNumericalIntegrator.) | |

Dimension |
Gets the number of dependent variables based on the
Dimension of the SystemOfEquations.
(Inherited from NumericalIntegrator.) | |

Direction |
Gets or sets whether to integrate forward, increasing the independent variable, or backward,
decreasing the independent variable.
(Inherited from NumericalIntegrator.) | |

FinalDependentVariableValues |
Gets or sets the values of the dependent variables resulting from the last integration step.
(Inherited from NumericalIntegrator.) | |

FinalIndependentVariableValue |
Gets or sets the value of the independent variable after an integration step.
(Inherited from NumericalIntegrator.) | |

InitialDependentVariableValues |
Gets or sets the values of the dependent variables prior to an integration step.
These values will be updated to the previous FinalDependentVariableValues
at the beginning of each integration step.
(Inherited from NumericalIntegrator.) | |

InitialIndependentVariableValue |
Gets or sets the value of the independent variable prior to an integration step.
(Inherited from NumericalIntegrator.) | |

InitialStepSize |
Gets or sets the initial (positive) size of the step to add to the InitialIndependentVariableValue
when performing an integration. By default, the initial value is one.
(Inherited from NumericalIntegrator.) | |

IsThreadSafe |
Gets a value indicating whether the methods on this instance are safe to call from
multiple threads simultaneously.
(Inherited from NumericalIntegrator.) | |

Iterations |
Gets or sets the number of iteration required to adapt the CurrentStepSize to
within error tolerance.
(Inherited from AdaptiveNumericalIntegrator.) | |

MaximumIterations |
Gets or sets the maximum number of Iterations to allow before forcing the integrator
to accept the CurrentStepSize and proceed to the next step.
(Inherited from AdaptiveNumericalIntegrator.) | |

MaximumStepSize |
Gets or sets the maximum size of the CurrentStepSize.
(Inherited from AdaptiveNumericalIntegrator.) | |

MinimumStepSize |
Gets or sets the (positive) minimum size of the CurrentStepSize.
(Inherited from AdaptiveNumericalIntegrator.) | |

PreviousStepSize |
Gets the size of the last step taken by the integrator. This returns the difference between the
FinalIndependentVariableValue and the InitialIndependentVariableValue.
(Inherited from NumericalIntegrator.) | |

RelativeTolerance |
Gets or sets the tolerance which provides a relative weight for the numerical error
based on the dependent variables. By default, this value is Epsilon13.
| |

StepDeflationExponent |
Gets or sets the exponent to apply to the error when calculating the amount to decrease the size of the step.
(Inherited from AdaptiveNumericalIntegrator.) | |

StepDeflationFactor |
Gets or sets a scalar multiplier to apply to the step when decreasing it.
(Inherited from AdaptiveNumericalIntegrator.) | |

StepInflationExponent |
Gets or sets the exponent to apply to the error when calculating the amount to increase the size of the step.
(Inherited from AdaptiveNumericalIntegrator.) | |

StepInflationFactor |
Gets or sets a scalar multiplier to apply to the step when increasing it.
(Inherited from AdaptiveNumericalIntegrator.) | |

StepSizeBehavior |
Gets or sets whether to avoid adapting the step size and instead fix the value of CurrentStepSize.
(Inherited from AdaptiveNumericalIntegrator.) | |

StepSizeInformation |
Gets or sets a value indicating whether the CurrentStepSize was changed from the InitialStepSize
and, if so, the nature of how it was changed.
(Inherited from NumericalIntegrator.) | |

StepTruncationOrder |
Gets or sets the integer exponent specifying the order of magnitude at which to
truncate the significant digits in the CurrentStepSize. For instance,
to truncate the value to three decimal places, specify a truncation order of -3.
To truncate the value to an order of 100, specify a truncation order of 2. To specify
the step size should be an integer value, specify a truncation order of 0.
(Inherited from AdaptiveNumericalIntegrator.) | |

SystemOfEquations |
Gets or sets the system of differential equations corresponding to the derivatives of the
dependent variables.
(Inherited from NumericalIntegrator.) | |

Tableau |
Gets or sets the Butcher Tableau with the coefficients and weights
to use to perform the RungeKutta integration.
(Inherited from RungeKuttaAdaptiveStepIntegrator.) |

Methods

Name | Description | |
---|---|---|

AdaptStep |
This method updates the CurrentStepSize to account for error in the state and its derivatives.
It returns true if the integrator should reintegrate with the updated step size or false if the integrator
should continue to the next integration step (potentially with a different step size).
(Overrides AdaptiveNumericalIntegratorAdaptStep.) | |

AdjustStep |
Adjusts a given step by increasing it or decreasing it based on the given error.
If the error is greater than one, the step will increase. Otherwise, it will decrease.
After adjusting the step, BoundAndTruncateStepSize(Double) is called.
(Inherited from AdaptiveNumericalIntegrator.) | |

BoundAndTruncateStepSize |
A method which should be called before updating the CurrentStepSize which
will bound the size based on the MinimumStepSize and MaximumStepSize,
and will truncate it based on the StepTruncationOrder.
(Inherited from AdaptiveNumericalIntegrator.) | |

Clone |
Create a copy of this integrator.
(Overrides NumericalIntegratorClone(CopyContext).) | |

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.) | |

GetType | Gets the Type of the current instance. (Inherited from Object.) | |

Initialize |
Initialize the integrator's initial independent and dependent variables and reset the integration parameters.
This should be called by the user prior to performing the first integration step.
(Overrides RungeKuttaAdaptiveStepIntegratorInitialize(Double, Double).) | |

Integrate | Perform an integration step moving the independent and dependent variables from their initial (the final values of the previous step) to their new final values, using the CurrentStepSize. When overriding this method, StartNextStep should be called prior to integration. | |

Integrate(Double) |
Integrate the current integration step with the given step size.
(Inherited from AdaptiveNumericalIntegrator.) | |

MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |

Reintegrate | Repeats the last integration of the differential equations. When overriding this method, note that the CurrentStepSize property should be unaffected by the stepSize parameter. | |

SetCurrentStepSize |
Sets the value of the CurrentStepSize which the
integrator will use for the next integration step.
(Inherited from AdaptiveNumericalIntegrator.) | |

StartNextStep |
This performs the task of setting the Initial values to the previous Final values prior to taking the next step.
This method is called prior to integrating the step but not called during reintegration.
(Inherited from NumericalIntegrator.) | |

ToString | Returns a string that represents the current object. (Inherited from Object.) |

Remarks

The coefficients used for this integrator come from a website of Jim Verner:
people.math.sfu.ca/~jverner/

See Also