Recent Research publications of Wayne Enright

Current Work Related to the Development of more Robust and Reliable ODE Methods

• Three seminars on ODE software presented at ANODE2001 in Auckland are given in NZ1, NZ2 and NZ3 . A paper which appeared in the proceedings of the same meeting and was also reprinted in Num. Alg. 32 (2002), is available here.
• A paper on superconvergent interpolants for collocation methods in ACM TOMS (Sept 2000) paper.
• A paper describing "Tools for the Verification of Approximate Solutions to Differential Equations" appeared in Handbook for Scientific Computation, (B. Einarsson ed.), SIAM Press and is available from here (2005). Another paper (presented at a workshop in Bari) appearing in JACM 185, (2006) describes the use of these verification tools and is is available from here.
• Two papers describing the development and use of more reliable and robust solvers for Differential Equations are available from here (APNUM, 56, 2006), and from here ( COLE, 1, 2006).
• Two recent presentations investigating the need and advantages in delivering more robust numerical solutions (at about twice the cost) have been presented at SciCADE07 where global error estimates and estimates of the conditioning of the underlying ODE are discussed, and at ICIAM07 where the cost associated with the more reliable error control is quantified and verified.

Current Work Related to Scientific Visualization:

• A general background seminar describing the basic problem is presented here (in postcript). A more specific seminar where the focus is on examples of where this approach can be applied and the implications for language-independent data structures is given here.
• Two papers describing this work are the ACM TOMS paper (2000), and the paper which appeared in the Proceedings of an IFIP WG2.5 WoConf8 (2001).
• A related investigation of how one can use this approach to develop fast contouring algorithms for visualizing approximate solutions of 2-dimensional PDEs is discussed in the paper to appear in ACM TOMS (2007). Similarly the use of this technique to accurately interpolate the solutions of 3-dimensional PDEs is investigated in the workshop presentation (September 2006).

  Contact Information:

  Phone: 416-978-5474
  e-mail: enright@cs.utoronto.ca