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 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
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 *      http://www.apache.org/licenses/LICENSE-2.0
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package org.apache.commons.math3.ode;

import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;

This interface represents a first order integrator for
differential equations.
The classes which are devoted to solve first order differential equations should implement this interface. The problems which can be handled should implement the FirstOrderDifferentialEquations interface.
See Also:
FirstOrderDifferentialEquations
StepHandler
EventHandler
Since:
1.2/** This interface represents a first order integrator for
 * differential equations.

 * <p>The classes which are devoted to solve first order differential
 * equations should implement this interface. The problems which can
 * be handled should implement the {@link
 * FirstOrderDifferentialEquations} interface.</p>
 *
 * @see FirstOrderDifferentialEquations
 * @see org.apache.commons.math3.ode.sampling.StepHandler
 * @see org.apache.commons.math3.ode.events.EventHandler
 * @since 1.2
 */

public interface FirstOrderIntegrator extends ODEIntegrator {

  
Integrate the differential equations up to the given time.
This method solves an Initial Value Problem (IVP).
Since this method stores some internal state variables made available in its public interface during integration (ODEIntegrator.getCurrentSignedStepsize()), it is not thread-safe.
Params:
equations – differential equations to integrate
t0 – initial time
y0 – initial value of the state vector at t0
t – target time for the integration
(can be set to a value smaller than t0 for backward integration)
y – placeholder where to put the state vector at each successful
 step (and hence at the end of integration), can be the same object as y0
Throws:
DimensionMismatchException – if arrays dimension do not match equations settings
NumberIsTooSmallException – if integration step is too small
MaxCountExceededException – if the number of functions evaluations is exceeded
NoBracketingException – if the location of an event cannot be bracketed
Returns:
stop time, will be the same as target time if integration reached its target, but may be different if some EventHandler stops it at some point./** Integrate the differential equations up to the given time.
   * <p>This method solves an Initial Value Problem (IVP).</p>
   * <p>Since this method stores some internal state variables made
   * available in its public interface during integration ({@link
   * #getCurrentSignedStepsize()}), it is <em>not</em> thread-safe.</p>
   * @param equations differential equations to integrate
   * @param t0 initial time
   * @param y0 initial value of the state vector at t0
   * @param t target time for the integration
   * (can be set to a value smaller than <code>t0</code> for backward integration)
   * @param y placeholder where to put the state vector at each successful
   *  step (and hence at the end of integration), can be the same object as y0
   * @return stop time, will be the same as target time if integration reached its
   * target, but may be different if some {@link
   * org.apache.commons.math3.ode.events.EventHandler} stops it at some point.
   * @exception DimensionMismatchException if arrays dimension do not match equations settings
   * @exception NumberIsTooSmallException if integration step is too small
   * @exception MaxCountExceededException if the number of functions evaluations is exceeded
   * @exception NoBracketingException if the location of an event cannot be bracketed
   */
  double integrate (FirstOrderDifferentialEquations equations,
                    double t0, double[] y0, double t, double[] y)
      throws DimensionMismatchException, NumberIsTooSmallException,
             MaxCountExceededException, NoBracketingException;

}