Algorithm 874: BACOLR—spatial and temporal error control software for PDEs based on high-order adaptive collocation

  • Authors:

  • R. Wang;P. Keast;P. H. Muir

  • Affiliations:

  • University of Saskatchewan;Dalhousie University, Nova Scotia, Canada;Saint Mary's University, Nova Scotia, Canada

  • Venue:
  • ACM Transactions on Mathematical Software (TOMS)
  • Year:
  • 2008

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Abstract

In this article we discuss a new software package, BACOLR, for the numerical solution of a general class of time-dependent 1-D PDEs. This package employs high-order adaptive methods in time and space within a method-of-lines approach and provides tolerance control of the spatial and temporal errors. The DAEs resulting from the spatial discretization (based on B-spline collocation) are handled by a substantially modified version of the Runge-Kutta solver, RADAU5. For each time step, the RADAU5 code computes an estimate of the temporal error and requires it to satisfy the user tolerance. After each time step BACOLR then computes a high-order estimate of the spatial error and requires this error estimate to satisfy the user tolerance. BACOLR was developed through a substantial modification of the adaptive method-of-lines package, BACOL. In this article we introduce the BACOLR package and present numerical results to show that the performance of BACOLR is comparable to and in some cases significantly superior to that of BACOL, which was shown in previous work to be more efficient, reliable and robust than other existing codes, especially for problems with solutions exhibiting narrow spikes or boundary layers.