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[Functions] source/numericalTools/RungeKutta/RungeKutta_step





  call RungeKutta_step (character (len=*), intent (in)  :: method,
                        function,          intent (in)  :: f,
                        real,              intent (in)  :: x,
                        real,              intent (in)  :: y     (:),
                        real,              intent (in)  :: eFrac,
                        real,              intent (in)  :: eBase (:),
                        real,              intent (in)  :: htry,
                        real,              intent (out) :: hused,
                        real,              intent (out) :: hnext,
                        real,              intent (out) :: yout  (:),
                        real,              intent (out) :: eout  (:))


  This routine performs a single adaptive Runge Kutta step. It copies the appropriate
  Butcher tableau data from the repository and calls the corresponding RK stepper.
  The details of the ODE function are contained in the passed array function 'f',
  which constitutes the link of the general Runge Kutta module to the individual
  applications. Thus 'f' has to be provided by an application outside of the Runge
  Kutta unit.

  The error vector for the dependent variables is composed of two pieces (as suggested
  by Numerical Recipies):

                            e (i) = eFrac * eBase (i)

  In this error vector definition, eFrac denotes the fractional value each of the
  individual eBase (i) values that define the total allowed maximum error for each
  of the i-th dependent variables.


  method       : the type of RK method to be applied
  f            : the ODE function containing details of the ODE system to be solved
  x            : the initial value of the independent variable
  y            : the initial values of the dependent variable(s)
  eFrac        : the fractional value for each of the error base values
  eBase        : the error base values for each of the dependent variables
  htry         : the initial step size on the independent variable
  hused        : the final step size applied on the independent variable
  hnext        : the suggested next step size on the independent variable
  yout         : the values of the dependent variable(s) after the accepted RK45 step
  eout         : the returned error of all dependent variable(s)


  Contains an interfaced function in the declarations (see below).