Fourth-order Runge-Kutta scheme


INTERFACE:

   subroutine runge_kutta_4(dt,numc,nlev,cc,right_hand_side)
DESCRIPTION:

Here, the fourth-order Runge-Kutta (RK4) scheme is coded, with four evaluations of the right hand sides per time step:

$\displaystyle \left. \begin{array}{rcl} c_i^{(1)} &=& \displaystyle c_i^n+\Delt...
...\left\{c_i^{(1)}+2c_i^{(2)}+2c_i^{(3)}+c_i^{(4)} \right\}. \end{array} \right\}$ (252)


USES:

   IMPLICIT NONE
INPUT PARAMETERS:
   REALTYPE, intent(in)                :: dt
   integer, intent(in)                 :: numc,nlev
  !INPUT/OUTPUT PARAMETER:
   REALTYPE, intent(inout)             :: cc(1:numc,0:nlev)
 
   interface
      subroutine right_hand_side(first,numc,nlev,cc,rhs)
         logical, intent(in)                  :: first
         integer, intent(in)                  :: numc,nlev
         REALTYPE, intent(in)                 :: cc(1:numc,0:nlev)
         REALTYPE, intent(out)                :: rhs(1:numc,0:nlev)
      end
   end interface
REVISION HISTORY:
   Original author(s): Hans Burchard, Karsten Bolding
LOCAL VARIABLES:
  logical  :: first
  REALTYPE :: rhs(1:numc,0:nlev),rhs1(1:numc,0:nlev)
  REALTYPE :: rhs2(1:numc,0:nlev),rhs3(1:numc,0:nlev)
  REALTYPE :: cc1(1:numc,0:nlev)
  integer  :: i,ci



Karsten Bolding 2012-12-28