Package com.imsl.math

Class ODE

java.lang.Object
com.imsl.math.ODE
All Implemented Interfaces:
Serializable, Cloneable
Direct Known Subclasses:
OdeAdamsGear, OdeRungeKutta
public abstract class ODE extends Object implements Serializable, Cloneable
ODE represents and solves an initial-value problem for ordinary differential equations.
See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final int
    AFTER_SUCCESSFUL_STEP
    Used by method examineStep to indicate examining after a successful step
    static final int
    AFTER_UNSUCCESSFUL_STEP
    Used by method examineStep to indicate examining after an unsuccessful step
    static final int
    BEFORE_STEP
    Used by method examineStep to indicate examining before the next step
    static final int
    ERROR_NORM_ABS
    Used by method setNorm to indicate that the error norm to be used is to be the absolute error, equals \(max(|e_i|)\)
    static final int
    ERROR_NORM_EUCLIDEAN
    Used by method setNorm to indicate that the error norm to be used is to be the scaled Euclidean norm defined as $${s = \sqrt {\sum_{i=1}^{neq}{\frac{{e_i}^2}{{w_i}^2}}}}$$ where \(w_i = e_i/max(|y_i(t)|,1.0)\) and \(neq\) is the number of equations
    static final int
    ERROR_NORM_MAX
    Used by method setNorm to indicate that the error norm to be used is to be the maximum of \(e_i/max(|y_i(t)|, floor)\) where floor is set via setFloor
    static final int
    ERROR_NORM_MINABSREL
    Used by method setNorm to indicate that the error norm to be used is to be the minimum of the absolute error and the relative error, equals the maximum of \(e_i/max(|y_i(t)|, 1)\)

  • Constructor Summary

    Constructors
    Constructor
    Description
    ODE()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    protected void
    examineStep(int state, double t, double[] y)
    Called before and after each internal step.
    double
    getFloor()
    Returns the value used in the norm computation.
    double
    getInitialStepsize()
    Returns the initial internal step size.
    double
    getMaximumStepsize()
    Returns the maximum internal step size.
    int
    getMaxSteps()
    Returns the maximum number of internal steps allowed.
    double
    getMinimumStepsize()
    Returns the minimum internal step size.
    int
    getNorm()
    Returns the switch for determining the error norm.
    double
    getScale()
    Returns the scaling factor.
    double
    getTolerance()
    Returns the error tolerance.
    void
    setFloor(double floor)
    Sets the value used in the norm computation.
    void
    setInitialStepsize(double stepsize)
    Sets the initial internal step size.
    void
    setMaximumStepsize(double stepsize)
    Sets the maximum internal step size.
    void
    setMaxSteps(int maxSteps)
    Sets the maximum number of internal steps allowed.
    void
    setMinimumStepsize(double stepsize)
    Sets the minimum internal step size.
    void
    setNorm(int normMethod)
    Sets the switch for determining the error norm.
    void
    setScale(double scale)
    Sets the scaling factor.
    void
    setTolerance(double tolerance)
    Sets the error tolerance.
    protected double
    vnorm(double[] v, double[] y, double[] ymax)
    Returns the norm of a vector.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • BEFORE_STEP

      public static final int BEFORE_STEP
      Used by method examineStep to indicate examining before the next step
      See Also:

    • AFTER_SUCCESSFUL_STEP

      public static final int AFTER_SUCCESSFUL_STEP
      Used by method examineStep to indicate examining after a successful step
      See Also:

    • AFTER_UNSUCCESSFUL_STEP

      public static final int AFTER_UNSUCCESSFUL_STEP
      Used by method examineStep to indicate examining after an unsuccessful step
      See Also:

    • ERROR_NORM_MINABSREL

      public static final int ERROR_NORM_MINABSREL
      Used by method setNorm to indicate that the error norm to be used is to be the minimum of the absolute error and the relative error, equals the maximum of \(e_i/max(|y_i(t)|, 1)\)
      See Also:

    • ERROR_NORM_ABS

      public static final int ERROR_NORM_ABS
      Used by method setNorm to indicate that the error norm to be used is to be the absolute error, equals \(max(|e_i|)\)
      See Also:

    • ERROR_NORM_MAX

      public static final int ERROR_NORM_MAX
      Used by method setNorm to indicate that the error norm to be used is to be the maximum of \(e_i/max(|y_i(t)|, floor)\) where floor is set via setFloor
      See Also:

    • ERROR_NORM_EUCLIDEAN

      public static final int ERROR_NORM_EUCLIDEAN
      Used by method setNorm to indicate that the error norm to be used is to be the scaled Euclidean norm defined as $${s = \sqrt {\sum_{i=1}^{neq}{\frac{{e_i}^2}{{w_i}^2}}}}$$ where \(w_i = e_i/max(|y_i(t)|,1.0)\) and \(neq\) is the number of equations
      See Also:

  • Constructor Details

    • ODE

      public ODE()

  • Method Details

    • examineStep

      protected void examineStep(int state, double t, double[] y)
      Called before and after each internal step. This method can be over-ridden by the user to examine intermediate values of t and y.
      Parameters:
      state - an int, one of BEFORE_STEP, AFTER_SUCCESSFUL_STEP or AFTER_UNSUCCESSFUL_STEP.
      t - double representing the independent variable.
      y - double array containing the dependent variables.

    • setFloor

      public void setFloor(double floor)
      Sets the value used in the norm computation.
      Parameters:
      floor - a double used in the norm computation. floor must be greater than zero.
      Default: floor = 1.0

    • setInitialStepsize

      public void setInitialStepsize(double stepsize)
      Sets the initial internal step size.
      Parameters:
      stepsize - a double specifying the initial internal step size. stepsize must be greater than or equal to zero. Default: stepsize = 0.0

    • setMaximumStepsize

      public void setMaximumStepsize(double stepsize)
      Sets the maximum internal step size.
      Parameters:
      stepsize - a double specifying the maximum internal step size. stepsize must be greater than zero.
      Default: See the setMaximumStepsize method in the subclasses for the default values used.

    • setMaxSteps

      public void setMaxSteps(int maxSteps)
      Sets the maximum number of internal steps allowed.
      Parameters:
      maxSteps - an int specifying the maximum number of internal steps allowed. maxSteps must be greater than zero. Default: maxSteps = 500

    • setMinimumStepsize

      public void setMinimumStepsize(double stepsize)
      Sets the minimum internal step size.
      Parameters:
      stepsize - a double specifying the minimum internal step size. stepsize must be greater than or equal to zero. Default: stepsize = 0.0

    • setNorm

      public void setNorm(int normMethod)
      Sets the switch for determining the error norm.
      Parameters:
      normMethod - an int specifying the switch for determining the error norm.
      Default: normMethod = ERROR_NORM_MINABSREL
      In the following table, \(e_i\) is the absolute value for an estimate of the error in \(y_i(t)\).

      normMethod Constraint
      ERROR_NORM_MINABSREL Minimum of the absolute error and the relative error, equals the maximum of \(e_i/max(|y_i(t)|, 1)\)
      ERROR_NORM_ABS Absolute error, equals \(max(e_i)\)
      ERROR_NORM_MAX Maximum of \(e_i/max(|y_i(t)|, floor)\)
      ERROR_NORM_EUCLIDEAN Scaled Euclidean norm defined as $${s = \sqrt {\sum_{i=1}^{neq}{\frac{{e_i}^2}{{w_i}^2}}}}$$ where \(w_i = e_i/max(|y_i(t)|,1.0)\) and \(neq\) is the number of equations

    • setScale

      public void setScale(double scale)
      Sets the scaling factor.
      Parameters:
      scale - a double specifying the scaling factor. scale must be greater than zero.
      Default: scale = 1.0

    • setTolerance

      public void setTolerance(double tolerance)
      Sets the error tolerance.
      Parameters:
      tolerance - a double specifying the error tolerance. tolerance must be greater than zero. Default: tolerance = 1.0e-6

    • getTolerance

      public double getTolerance()
      Returns the error tolerance.
      Returns:
      a double specifying the error tolerance.

    • getInitialStepsize

      public double getInitialStepsize()
      Returns the initial internal step size.
      Returns:
      a double specifying the initial internal step size.

    • getMinimumStepsize

      public double getMinimumStepsize()
      Returns the minimum internal step size.
      Returns:
      a double specifying the minimum internal step size.

    • getMaximumStepsize

      public double getMaximumStepsize()
      Returns the maximum internal step size.
      Returns:
      a double specifying the maximum internal step size.

    • getScale

      public double getScale()
      Returns the scaling factor.
      Returns:
      a double specifying the scaling factor.

    • getNorm

      public int getNorm()
      Returns the switch for determining the error norm.
      Returns:
      an int specifying the switch for determining the error norm. In the following, \(e_i\) is the absolute value for an estimate of the error in \(y_i(t)\).

      normMethod Constraint
      ERROR_NORM_MINABSREL Minimum of the absolute error and the relative error, equals the maximum of \(e_i/max(|y_i(t)|, 1)\)
      ERROR_NORM_ABS Absolute error, equals \(max(e_i)\)
      ERROR_NORM_MAX Maximum of \(e_i/max(|y_i(t)|, floor)\)
      ERROR_NORM_EUCLIDEAN Scaled Euclidean norm defined as $${s = \sqrt {\sum_{i=1}^{neq}{\frac{{e_i}^2}{{w_i}^2}}}}$$ where \(w_i = e_i/max(|y_i(t)|,1.0)\) and \(neq\) is the number of equations

    • getFloor

      public double getFloor()
      Returns the value used in the norm computation.
      Returns:
      a double used in the norm computation.

    • getMaxSteps

      public int getMaxSteps()
      Returns the maximum number of internal steps allowed.
      Returns:
      an int specifying the maximum number of internal steps allowed.

    • vnorm

      protected double vnorm(double[] v, double[] y, double[] ymax)
      Returns the norm of a vector. This method can be over-ridden by the user to supply a different norm than those available through setNorm.
      Parameters:
      v - a double array containing the vector whose norm is to be computed
      y - a double array containing the values of the dependent variable
      ymax - a double array containing the maximum y values computed thus far
      Returns:
      a double scalar value representing the norm of the vector v