Error control Gaussian collocation software for boundary value ODEs and 1D time-dependent PDEs

Error control software packages based on Gaussian collocation have been widely used for the numerical solution of boundary value ODEs (BVODEs) and 1D parabolic time-dependent PDEs (1D PDEs) for several decades. These robust and efficient packages are among the best available for these problem classes. In this paper, we survey error control Gaussian collocation software for BVODEs and 1D PDEs and provide an overview of recent work involving the development of two new packages, one for each problem class. The first is an updated version of the well-known COLSYS/COLNEW package for BVODEs. The second is the newest member of the BACOL family of software packages for 1D PDEs. We briefly review the underlying numerical algorithms employed in these packages and then provide numerical results that show the superiority of the new packages compared to previously released packages from each software class.