Runge |
The core implements functionality common to all Runge-Kutta methods, such as stepping, error evaluation, interpolation, and initial step-size estimation.
Inheritance HierarchyNamespace: Altaxo.Calc.Ode
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)
SyntaxC#
protected class Core
The RungeKuttaExplicitBaseCore type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | RungeKuttaExplicitBaseCore | Initializes a new instance of the RungeKuttaExplicitBaseCore class. |
Properties| Name | Description | |
|---|---|---|
 | AbsoluteTolerance | Gets or sets the absolute tolerance. |
| AbsoluteTolerances | Gets or sets the absolute tolerances. It must be ensured that this array is not altered. |
| BHML | Sets the coefficients for the error evaluation. These coefficients are the difference of the high-order and low-order bottom side coefficients of the Runge-Kutta scheme. If set to , local error calculation (and thus automatic step size control) is not possible. |
| ErrorNorm | Gets the vector norm used to reduce the vector of relative errors (dimension N) to a scalar relative error. |
| InterpolationCoefficients | Gets or sets the interpolation coefficients for dense output. |
| RelativeTolerance | Gets or sets the relative tolerance. |
| RelativeTolerances | Gets or sets the relative tolerances. It must be ensured that this array is not altered. |
| StepSizeFilter | Gets or sets the step size filter. For the values see StepSizeFilter. |
| StiffnessDetectionEveryNumberOfSteps | Gets or sets the number of successful steps between tests for stiffness. Setting this value to 0 disables stiffness detection. The default value is 0. |
| StiffnessDetectionThresholdValue | Sets the stiffness detection threshold value. |
| X | Gets the current value of x. |
| X_previous | Gets the value of x before the last step. |
| Y_volatile | Gets the current values of the variables. Attention: the returned array will change the next time you call EvaluateNextSolutionPoint(Double). Therefore, if you do not intend to use the values immediately, make a copy of this array! |
Methods| Name | Description | |
|---|---|---|
| Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
| EvaluateNextSolutionPoint | Evaluates the next solution point in one step. To get the results, see X and Y_volatile. |
 | 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 an interpolated point in the last evaluated interval. Please use the result immediately, or else make a copy of the result, since an internal array is returned, which is overwritten at the next operation. |
| GetRecommendedStepSize | Gets the recommended step size. |
| GetRelativeError_InfinityNorm | Gets the relative error by the infinity norm, which should be in the order of 1 if the step size is optimally chosen. |
| GetRelativeError_L2Norm | Gets the relative error calculated by the L2-norm, which should be in the order of 1 if the step size is optimally chosen. |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| Revert | Reverts the state of the instance to the former solution point by setting X to X_previous and reverting Y_volatile. |
| SetCoefficientsForAdditionalStages | Sets the coefficients for additional stages that are necessary for dense output (interpolation). |
| ThrowIfStiffnessDetected | Called after every successful step. Detects a stiffness condition. If one is found, an exception is thrown. |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
Fields| Name | Description | |
|---|---|---|
 | _a | Central coefficients of the Runge-Kutta scheme. See [1], page 135. |
| _a_interpolation | Additional central coefficients of the Runge-Kutta scheme optionally needed for interpolation. |
 | _absoluteTolerances | The absolute tolerances. 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 as y. |
| _b | High order bottom side coefficients of the Runge-Kutta scheme. |
| _bhml | Differences between high order and low order bottom side coefficients of the Runge-Kutta scheme (for error estimation). |
| _c | Left side coefficients of the Runge-Kutta scheme (partitions of the step). |
| _c_interpolation | Additional left side coefficients of the Runge-Kutta scheme optionally needed for dense output (partitions of the step). |
| _f | The ODE function. |
| _interpolationCoefficients | The interpolation coefficients. Note that zero to third order is calculated from the y values and slopes at the start and end of the step. Thus, these coefficients only have to cover the orders 4..n of the interpolation. |
| _isDenseOutputPrepared | True if dense output was prepared, i.e. the array _rcont contains valid values. |
| _isFirstSameAsLastMethod | if the method has the FSAL (first-same-as-last) property; otherwise, . This is, for instance, true for the Dormand-Prince (RK547M) method. |
| _isKnextEvaluated | Designates whether the slope at y_current was evaluated (for non-FSAL methods). For FSAL methods, this value is meaningless, because the last stage always contains k_next after a step. |
| _k | Array of derivatives at the different stages. |
| _numberOfAdditionalStagesForDenseOutput | The number of additional stages for dense output of high order. |
| _numberOfNonstiffEvaluationResults | The number of evaluation results in ThrowIfStiffnessDetected for which the result was false (non-stiff). This counter is reset to zero if a stiff condition is detected. |
| _numberOfRejectedStiffnessDetectionCalls | The number of rejected stiffness detection calls after the last stiffness evaluation. |
| _numberOfStages | The number of stages of this method. |
| _numberOfStiffEvaluationResults | The number of evaluation results in ThrowIfStiffnessDetected for which the result was true (stiff). This counter is reset to zero if a non-stiff condition is detected. |
| _order | Order of the Runge-Kutta method (the highest order of the embedded pair). |
| _rcont | Contains the precalculated polynomial coefficients for dense output. |
| _relativeTolerances | The relative 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 as y. |
| _stepSize_current | Step size of the current step. |
| _stepSize_previous | Step size of the previous step. |
| _stepSizeFilter | The step size filter. |
| _stiffnessDetectionEveryNumberOfSteps | Number of successful steps between calls to stiffness detection. If this value is 0, stiffness detection is disabled. |
| _stiffnessDetectionThresholdValueSquared | Squared value of the stiffness detection threshold. |
| _wasSolutionPointEvaluated | True if at least one solution point was evaluated. |
| _x_current | X value at the end of the current step. |
| _x_previous | X value at the begin of the current step. |
| _y_current | Y values at the end of the current step. |
| _y_current_LocalError | Contains the array of local errors. |
| _y_previous | Y values at the beginning of the current step. |
| _y_stages | Array to accommodate y for calculation of the stages. At the end of EvaluateNextSolutionPoint(Double), this array usually contains the y of the last stage (for non-FSAL methods), or the y of the stage before the last stage (FSAL methods). |
 | StepSize_MaxFactor | Maximum factor by which the step size can be increased. |
| StepSize_MinFactor | Minimum factor by which the step size can be decreased. |
| StepSize_SafetyFactor | Safety factor for the step size. |
See Also