Abstract
BACOL is a new, high quality, robust software package in Fortran 77
for solving one-dimensional parabolic PDEs, which has been shown
to be significantly more efficient than any other widely available
software package of the same class ( to our knowledge), especially
for problems with solutions exhibiting rapid spatial variation. A
novel feature of this package is that it employs high order, adaptive
methods in both time and space, controlling and balancing both spatial
and temporal error estimates. The software implements a spline collocation
method at Gaussian points, with a B-spline basis, for the spatial
discretization. The time integration is performed using a modification
of the popular DAE solver, DASSL. Based on the computation of a second,
higher order, global solution, a high quality a posteriori spatial
error estimate is obtained after each successful time step. The spatial
error is controlled by a sophisticated new mesh selection algorithm
based on an equidistribution principle. In this article we describe
the overall structure of the BACOL package, and in particular the
modifications to the DASSL package that improve its performance within
BACOL. An example is provided in the online Appendix to illustrate
the use of the package.
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