psol_banpre Subroutine

   pure subroutine psol_banpre( &
      neq, t, y, ydot, savr, wk, cj, wght, rwp, iwp, b, epslin, ierr, rpar, ipar)
   !! This routine solves the linear system \(P x = b\) for the banded preconditioner \(P\),
   !! given a vector \(b\), using the LU decomposition produced by [[jac_banpre]]. The solution
   !! is carried out by [[dgbsl]] from LINPACK.

      use linpack, only: dgbsl

      integer, intent(in) :: neq
        !! Problem size.
      real(rk), intent(in) :: t
        !! Current independent variable (not used).
      real(rk), intent(in) :: y(*)
        !! Current dependent variables (not used).
      real(rk), intent(in) :: ydot(*)
        !! Current derivatives of dependent variables (not used).
      real(rk), intent(in) :: savr(*)
        !! Current residual evaluated at `(t, y, ydot)` (not used).
      real(rk), intent(in) :: wk(*)
        !! Real work space available to this subroutine (not used).
      real(rk), intent(in) :: cj
        !! Scalar used in forming the system Jacobian (not used).
      real(rk), intent(in) :: wght(*)
        !! Error weights for computing norms (not used).
      real(rk), intent(inout) :: rwp(*)
        !! Real work array containing the LU decomposition of \(P\).
      integer, intent(inout) :: iwp(*)
        !! Integer array containing matrix pivot information.
      real(rk), intent(inout) :: b(*)
        !! Right-hand side vector on input; solution on output.
      real(rk), intent(in) :: epslin
        !! Tolerance for linear system (not used).
      integer, intent(inout) :: ierr
        !! Error flag.
      real(rk), intent(inout) :: rpar(*)
        !! Real array used for communication between the calling program and user routines
        !! (not used).
      integer, intent(inout) :: ipar(*)
        !! Integer array used for communication between the calling program and user routines 
        !! (not used).
      
      integer :: meband, ml, mu

      ml = ipar(1)
      mu = ipar(2)
      meband = 2*ml + mu + 1
      
      ierr = 0
      call dgbsl(rwp, meband, neq, ml, mu, iwp, b, 0)

   end subroutine psol_banpre