Error Control B-spline Gaussian Collocation/Runge-Kutta PDE Software with Interpolation-based Spatial Error Estimation

Jack Pew, Tom Murtha, Connor Tannahill, Paul Muir

ABSTRACT
This report considers a family of software packages for the error controlled
numerical solution of systems of one-dimensional partial differential
equations. B-spline Gaussian collocation is used for the spatial discretiza-
tion; the time integration is performed in the two earliest members of
this family, BACOL and BACOLR, using multi-step and Runge-Kutta
methods, respectively. BACOLR was shown to have better performance
than BACOL for problems where the multi-step methods have stability
issues. The recently released third member of this family, called BACOLI,
is a modification of BACOL that improves the efficiency of the spatial er-
ror estimation computation by introducing two new interpolation-based
schemes. In this report, we consider the newest member of this fam-
ily, BACOLRI, a modification of BACOLR, that combines the improved
Runge-Kutta stability of the time integration employed by BACOLR with
the improved efficiency of the interpolation-based spatial error estimation
schemes employed by BACOLI. We describe the modifications undertaken
to obtain BACOLRI from BACOLR and provide extensive numerical re-
sults to compare the performances of the two packages.