@Article{Pew:2015:ABB,
  author =       "Jack Pew and Zhi Li and Paul Muir",
  title =        "Algorithm xxx: {BACOLI}: {B-spline} Adaptive Collocation
                  Software for {PDEs} with Interpolation-based Spatial Error 
		  Control",
  journal =      "{ACM} Transactions on Mathematical Software",
  accepted =     "23 August 2015",
  upcoming =     "true", 
  abstract =     "
                  BACOL and BACOLR are (Fortran 77) B-spline adaptive
                  collocation  packages for the numerical solution of
                  1D parabolic PDEs. The packages have been shown to
                  be  superior to other similar packages, especially for
                  problems exhibiting sharp, moving spatial layer regions,
                  where a stringent tolerance is imposed.  In addition to
                  providing temporal error control through the time-stepping
                  software, BACOL and BACOLR feature control of a high order
                  estimate of the spatial error of the approximate solution,
                  obtained by computing a {\it second\/} approximate solution
                  of one higher order of accuracy; the cost is substantial -
                  execution time and memory usage are almost doubled.
                
                  In this paper we discuss BACOLI, a new version of BACOL
                  that computes only one approximate solution and uses
                  efficient interpolation-based schemes to obtain a spatial
                  error estimate.  In previous studies these schemes have
                  been shown to provide spatial error estimates of comparable
                  quality to those of BACOL\@.  We describe the substantial
                  modification of BACOL  needed to obtain BACOLI, and provide
                  numerical results   showing that BACOLI is significantly more
                  efficient than BACOL, in some cases by as much as a factor
                  of two.  We also introduce a Fortran 95 wrapper for BACOLI
                  (called BACOLI95) and discuss its simplified user-interface.",
}