BulirschStoerIntegrator Class

An adaptive numerical integrator which uses successive subdivisions of the specified step size in order to measure the relative error in order to update the step size.

Note that the Tolerance will affect both how accurate the integrator will be as well as how small the step size will be to achieve the desired accuracy. Having a really small tolerance in relation to large dependent variables may not be best, since it may drive the step size to values near zero over the course of the integration when a higher tolerance will still yield accurate results.

Inheritance Hierarchy

SystemObject
  AGI.Foundation.NumericalMethodsNumericalIntegrator
    AGI.Foundation.NumericalMethods.AdvancedAdaptiveNumericalIntegrator
      AGI.Foundation.NumericalMethodsBulirschStoerIntegrator

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 BulirschStoerIntegrator : AdaptiveNumericalIntegrator

Public Class BulirschStoerIntegrator
	Inherits AdaptiveNumericalIntegrator

public ref class BulirschStoerIntegrator : public AdaptiveNumericalIntegrator

type BulirschStoerIntegrator =  
    class
        inherit AdaptiveNumericalIntegrator
    end

The BulirschStoerIntegrator type exposes the following members.

Constructors

	Name	Description
	BulirschStoerIntegrator	Initializes a new instance. Be sure to set the SystemOfEquations before integrating.
	BulirschStoerIntegrator(DependentVariableDerivatives)	Initializes a new instance.
	BulirschStoerIntegrator(BulirschStoerIntegrator, CopyContext)	Initializes a new instance as a copy of an existing instance.

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Properties

	Name	Description
	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.)
	LastNumberOfSubdivisionsUsed	Gets the current maximum number of subdivisions used during the last iteration step.
	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.)
	SafetyFactorOne	Gets or sets a safety factor used when analyzing roundoff error and determining the new step size. The equation for the step size update is: Hnew = S1 * H * (S2 / Error)^-(2k+1) where "H" is the step size, "Error" is the roundoff error, and "k" is the iteration index into the Subdivisions array. The default value is 1/4.
	SafetyFactorTwo	Gets or sets a safety factor used when analyzing roundoff error and determining the new step size. The equation for the step size update is: Hnew = S1 * H * (S2 / Error)^-(2k+1) where "H" is the step size, "Error" is the roundoff error, and "k" is the iteration index into the Subdivisions array. The default value is 7/10.
	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.)
	Subdivisions	Gets or sets the set of successive subdivisions used to take steps. For each step the Bulirsch-Stoer integrator takes, it will divide the step size according to the subdivisions and analyze the error. If the error doesn't converge, it will continue to subdivide until it either converges or decides that the step size itself is problematic and starts over with a new step size. The default set is derived from the work of Deuflhard: { 2, 4, 6, 8, 10 } When changing the set, make sure to check for stability as having too few or too many subdivisions can change the behavior of the algorithm.
	SystemOfEquations	Gets or sets the system of differential equations corresponding to the derivatives of the dependent variables. (Inherited from NumericalIntegrator.)
	Tolerance	Gets or sets the value for the tolerance used to scale the error control, which will control both how accurate the integrator is and the step size used during integration.

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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 AdaptiveNumericalIntegratorInitialize(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. (Overrides NumericalIntegratorReintegrate(Double).)
	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. (Overrides NumericalIntegratorStartNextStep.)
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Reference

AGI.Foundation.NumericalMethods Namespace