Tolerance vs. Error Results for a Class of Error
Control B-spline Gaussian Collocation PDE Solvers
  
           Paul Muir and Jack Pew
  
ABSTRACT
B-spline Gaussian collocation software for the numerical solution of partial
differential equations has been widely used for several decades. BACOL and
BACOLI are recently developed packages of this class that provide control of estimates
of the temporal and spatial errors of the numerical solution through the use
of adaptive time-stepping/method order selection and adaptive spatial mesh refinement.
Several previous studies have investigated the performance of the BACOL and
BACOLI packages with respect to work-accuracy, i.e., efficiency, measures. In this
report, we investigate the reliability of the BACOL and BACOLI packages, focusing
on the relationship between the requested tolerance and the accuracy achieved. In
particular, we consider the effect, on the reliability of the software, of (i) the degree
of the piecewise polynomials employed in the representation of the spatial dependence
of the approximate solution, (ii) the type of spatial error control employed,
and (iii) the type of spatial error estimate computed.