Algorithm 962: BACOLI: B-spline Adaptive Collocation Software for PDEs with Interpolation-Based Spatial Error Control

BACOL and BACOLR are (Fortran 77) B-spline adaptive collocation packages for the numerical solution of 1D parabolic Partial Differential Equations (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 timestepping software, BACOL and BACOLR feature control of a high-order estimate of the spatial error of the approximate solution, obtained by computing a second approximate solution of one higher order of accuracy; the cost is substantial—execution time and memory usage are almost doubled.

In this article, 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 2. We also introduce a Fortran 95 wrapper for BACOLI (called BACOLI95) and discuss its simplified user interface.