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

Namespace: AGI.Foundation.NumericalMethods
Assembly: AGI.Foundation.Core (in AGI.Foundation.Core.dll) Version: 24.2.419.0 (24.2.419.0)

Syntax

C++

Copy

public class RungeKuttaVerner89Integrator : RungeKuttaAdaptiveStepIntegrator

Public Class RungeKuttaVerner89Integrator
	Inherits RungeKuttaAdaptiveStepIntegrator

public ref class RungeKuttaVerner89Integrator : public RungeKuttaAdaptiveStepIntegrator

type RungeKuttaVerner89Integrator =  
    class
        inherit RungeKuttaAdaptiveStepIntegrator
    end

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.

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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.)

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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. (Inherited from AdaptiveNumericalIntegrator.)
	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. (Inherited from RungeKuttaAdaptiveStepIntegrator.)
	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.)

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Remarks

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

Reference

AGI.Foundation.NumericalMethods Namespace