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.
Namespace: AGI.Foundation.NumericalMethods
The BulirschStoerIntegrator type exposes the following members.
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. 
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 BulirschStoer 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.

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