	Name	Description
	GearsBDFWithNordsieckStateCore(Double, Double, ActionDouble, Double, Double, MultiStepMethodBaseCalculateJacobian, OdeMethodOptions)	Initializes a new instance of the GearsBDFWithNordsieckStateCore class. The initial step size is 1.
	GearsBDFWithNordsieckStateCore(Double, Double, ActionDouble, Double, Double, MultiStepMethodBaseCalculateJacobian, OdeMethodOptions)	Initializes a new instance of the GearsBDFWithNordsieckStateCore class (mostly for testing purposes, since the kth derivatives at the starting point must be known in advance). The initial step size is 1.

	Name	Description
	EvaluateJacobian	Gets or sets the function to evaluate the jacobian.
	MaxOrder	Gets or sets the maximum allowed order.
	MinOrder	Gets or sets the minimum allowed order.
	NumberOfJacobianEvaluations	Gets the number of jacobian evaluations so far.
	NumberOfStepsTaken	Gets the number of steps taken so far.
	X	Gets the current x value.
	Y_volatile	Gets the current y values. The elements of the returned array must not be changed, and are intended for immediate use only.

	Name	Description
	AdjustStepSizeAndOrder	Compares the errors at the current order q, at order (q-1) and at order (q+1), using the proposed step sizes at these orders. The order which maximizes the step size is then chosen, and the step size is adjusted accordingly.
	Calculate_En_Q	Calculates the relative error En for the current order q. See eq. 2.41 in [1].
	Calculate_En_QMinus1	Calculates the relative error En(q-1) for the next lower order (q-1).
	Calculate_En_QPlus1	Calculates the relative error En(q+1) for the next higher order (q+1).
	CalculateOnePlusProducts_tn	Calculates the product of the differences of previous x (the term in square brackets in eqs. 2.40, 2.41 and 2.44 in Byrne and Hindmarsh [1]).
	ChangeStepSize	Changes the size to a new value.
	ComputeCoefficients_L	Computes the coefficients l. l is used to update the Nordsieck vector if the error vector is known: z_n = z_n0 + e_n * l with e_n = y_n - y_n0.
	Correct	Corrects the Nordsieck array using the corrected y values and the l array. See eq. 2.19 in [1].
	DecreaseOrderBy1	Decreases the order by 1. This method scales the Nordsieck array by the polynomial coefficients of eq. 2.49 in Byrne and Hindmarsh [1].
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object)
	EvaluateNextSolutionPoint	Evaluates the next solution point.
	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.
	GetInterpolatedY_volatile	Gets interpolated y values. The independent variable x must lie inbetween the x of the previous step and the current step.
	GetProposedStepSizeFactorClamped	Gets the proposed step size factor (clamped). This clamped version should be used for step size control. For comparison of the errors of order q-1, q, and q+1, use the unclamped version.
	GetProposedStepSizeFactorUnclamped	Gets the proposed step size factor (unclamped). This unclamped version should only be used for comparison of the errors of order q-1, q, and q+1. Use the clamped version for step size control.
	GetRelativeError_InfinityNorm	Gets the relative error (Infinity norm) from the absolute errors. The absolute errors are given by en - Qn * enm1.
	GetRelativeError_L2Norm	Gets the relative error (L2 norm) from the absolute errors. The absolute errors are given by en - Qn * enm1.
	GetType	Gets the Type of the current instance. (Inherited from Object)
	IncreaseOrderBy1	Increases the order by 1. It is ensured that the Nordsieck state can accomodate the new derivative. The new derivative itself is set to zero. See the notes below eq. 2.49 in Byrne and Hindmarsh [1].
	IterationUsingFunctionalIteration	Does some iteration steps. This iteration method does not use the Jacobian for Newton-Raphson steps, instead a functional iteration is executed. This takes much longer to reach the same degree of accuracy. At the end, the corrected y-values are stored in _aux1.
	IterationUsingJacobian	Does some iteration steps. At the end, the corrected y-values are stored in _aux1.
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object)
	OptimizeStepSizeForNextMandatoryPoint	Optimizes the step size, in a way that the next mandatory solution point will be reached without too big or too small step sizes.
	Predict	Calculates a first guess of the new Nordsieck state from the old state, and advances the _x array to the new point.
	RestoreNordsieckState	Restores the Nordsieck state ( copies back from _nordsieckArray_Saved to _nordsieckArray, restores _nordsieckArray_h, and also restores the history of x values in _x.
	SaveNordsieckState	Saves the Nordsieck state (makes a copy from _nordsieckArray to _nordsieckArray_h_Saved), and saves the value of the step size in _nordsieckArray_h_Saved).
	ScaleStepSize	Scales the step size by a factor.
	ToString	Returns a string that represents the current object. (Inherited from Object)

	Name	Description
	_absoluteTolerances	The absolute tolerance. This is either an array of length 1 (in this case the absolute tolerances of all y values are equal), or an array of the same size than y.
	_en_current	The current error array, i.e. the difference between the iterated y and the first estimation of y of the current step. See eq. 2.12 in Byrne/Hindmarsh 1975 [1].
	_en_previous	The previous error array, i.e. the difference between the iterated y and the first estimation of y of the previous step. See eq. 2.12 in Byrne/Hindmarsh 1975 [1].
	_errorNorm	The vector norm, by which from the vector of relative errors (dimension N) the scalar relative error is calculated.
	_f	The differential equation to integrate. First arg is the independent variable (x), second arg are the current y-values, and the 3rd arg adopts the derivatives of y as calculated by this function.
	_iterationMethod
	_relativeTolerances	The relativ tolerances. This is either an array of length 1 (in this case the relative tolerances of all y values are equal), or an array of the same size than y.
	_x	Array of previous x. x[0] is the current x, x[1] is the previous x and so on.

GearsBDFWithNordsieckStateCore Class

Reference