**Selected Publications: (Please
contact Paul Muir (****muir@smu.ca****) for further
info)**

J. Pew, Z. Li, P.H. Muir, *Algorithm** 962: BACOLI: B-spline
Adaptive Collocation Software for PDEs with Interpolation-based Spatial Error
Control*, ACM Trans. on Math. Softw., 42, 3, Article 25, 2016.

P.H. Muir and J. Pew, *Recent Advances
in Error Control B-spline Gaussian Collocation
Software for PDEs*, Interdisciplinary Topics in Applied Mathematics,
Modeling and Computational Science, Springer Proceedings in Mathematics &
Statistics, 117, M. Cojocaru, I.S. Kotsireas, R. Makarov, R. Melnik, H. Shodiev, (Eds.), Springer, 2015, pp. 329-334. *Reprint available upon request.*

J. Pew, P.H. Muir, J. Wang, T. Frasier, *Related:
an R Package for Analysing Pairwise
Relatedness from Codominant Molecular Markers*,
Mol. Ecol. Resour., 15, 2015, pp. 557-561. *Reprint available upon request.*

J. Ivanoff, R. Blagdon,
S. Feener, M. McNeil, P.H. Muir, *On the Temporal
Dynamics of Spatial Stimulus Response Transfer between Spatial Incompatibility
and Simon Tasks*, Front. Neurosci., 8, 2014,
Article 243.

P.H. Muir, *B-spline Gaussian Collocation Software for 1D
Parabolic PDEs*, Proceedings of the
8th International Conference on
Scientific Computing and Applications, AMS Contemporary Mathematics, 586, 2013,
pp. 267-276.

Z. Li and P.H. Muir, *B-Spline
Collocation Software for Two-Dimensional, Time-Dependent Parabolic PDEs*,
Advances in Applied Mathematics and Mechanics, 5, 4, 2013, pp. 528-547.

J.J. Boisvert, P.H. Muir and R.J. Spiteri, *A** Fortran95 Runge-Kutta BVODE Solver with Defect and Global Error
Control*, ACM Trans. Math. Softw., 39, 2, 2013, Article 11. *Reprint available upon request.*

R.C. McKay, T. Kolokolnikov, P.H. Muir, *Interface Oscillations in Reaction-Diffusion Systems beyond the Hopf Bifurcation*,
Discrete and Continuous Dynamical Systems - Series B, 17, 7, 2012, pp.
2523-2543. *Reprint
available upon request.*

T. Arsenault, T. Smith, P.H. Muir, J. Pew, *Asymptotically Correct
Interpolation-based Spatial Error Estimation for 1D PDE Solvers*,
Canadian Applied Mathematics Quarterly, 20, 3, 2012, pp. 307-328.

J.J. Boisvert, P.H. Muir and R.J. Spiteri, *py_bvp**: A Universal
Python Interface For BVP Code, *Proceedings of the* *High Performance Computing Symposium (HPC 2010), 2010.

W.H. Enright and P.H. Muir, *New Interpolants for Asymptotically Correct
Defect Control of BVODEs, *Numerical Algorithms 53, 2, 2010, pp. 219-238. *Reprint available upon
request.*

T. Arsenault, T. Smith, P.H. Muir, *Superconvergent Interpolants for Efficient Spatial Error Estimation in 1D
PDE Collocation Solvers, *Canadian Applied Mathematics Quarterly, 17, 3,
2009, pp. 409-431.

R.
Wang, P. Keast, P.H. Muir, *Algorithm** 874: BACOLR - Spatial and Temporal Error Control Software for PDEs
based on High Order Adaptive Collocation*, ACM Trans. Math. Softw.,
34, Article No. 15, 2008. *Reprint
available upon request.*

L.F.
Shampine, P.H. Muir, H. Xu,
*A
user-friendly Fortran BV P solver,* J. Numer. Anal. Indust. Appl. Math., 1, 2006, 201217.

R.
Wang, P. Keast, P.H. Muir, *BACOL: B-spline adaptive COLlocation
software for 1-D parabolic PDEs*, ACM Trans. Math. Softw., 30, 2004, 454--470. *Reprint available upon
request.*

R. Wang,
P. Keast, P.H. Muir, *A high-order global spatially
adaptive collocation method for 1-D parabolic PDEs*, Appl. Numer. Math., 50,
2004, 239--260. *Reprint available upon request.*

R.
Wang, P. Keast, P.H. Muir, *A comparison of adaptive software for 1-D
parabolic PDEs*, J. Comput. Appl.
Math., 169, 2004, 127--150.

L.F.
Shampine and and P.H. Muir,
*Estimating
conditioning of BVPs for ODEs*, Math. Comput. Modelling, 40, 2004,
1309--1321.

A.M. Hynick, P. Keast,
and P.H. Muir, *Pulse detection software for Initial Value
ODEs*, Math. Comput. Modelling, 40, 2004, 1335--1350.

P.H.
Muir, R.N. Pancer, K.R. Jackson, *PMIRKDC: a
parallel mono-implicit Runge-Kutta code with defect
control for boundary value ODEs*, Parallel Comput.,
29, 2003, 711-741. *Reprint
available upon request.*

P.H. Muir and M. Adams, *Mono-implicit
Runge-Kutta-Nystrom methods for boundary value
ordinary differential equations*, BIT, 41, 2001, 775-798. *Reprint available upon request.*

S.D. Jackson and P.H. Muir, *Theory
and numerical simulation of nth-order cascaded Raman fiber lasers*, J. Opt.
Soc. Am. B, 18, 2001, 1297-1306. *Reprint available upon request.*

W.H. Enright and P.H. Muir, *Superconvergent** interpolants for
discrete collocation solutions*, SIAM J. Sci. Comp., 21, 1999, 227-254. *Reprint available upon request.*

D.
Voss and P.H. Muir, *Mono-implicit Runge-Kutta
schemes for the parallel solution of initial value problems*, J. Comp.
Appl. Math., 102, 1999, 235-252.

P.H.
Muir, *Optimal discrete and continuous
mono-implicit Runge-Kutta schemes for boundary value
ODEs*, Adv. Comp. Math., 10, 1999, 135-167. *Reprint available upon request.*

T.B.
Nokonechny, P. Keast, and
P.H. Muir, *A method of lines package, based on monomial
spline collocation, for systems of one-dimensional
parabolic differential equations*, in ``Numerical Analysis, A.R.
Mitchell, 75th Birthday Volume", Eds. D.F. Griffiths and G.A. Watson,
World Scientific, London, 1996, 207-223.

W.H.
Enright and P.H. Muir, *Runge-Kutta** software with defect control for boundary value ODEs*, SIAM J. Sci.
Comput., 17, 1996, 479-497. *Reprint available upon request.*

P.H.
Muir, *A note on continuous Runge-Kutta schemes with sub-optimal stage orders*, Congressus Numerantium, 106, 1995,
105-118.

P.H.
Muir and K. Remington, *A parallel
implementation of a Runge-Kutta code for systems of
nonlinear boundary value ODEs*, Congressus Numerantium, 99, 1994, 291-305.

K.
Burrage, F.H. Chipman, P.H.
Muir, *Order results for mono-implicit Runge-Kutta methods*, SIAM J. Numer.
Anal., 31, 1994, 876-891. *Reprint
available upon request.*

P.H. Muir and B. Owren, *Order barriers
and characterizations for continuous mono-implicit Runge-Kutta
schemes*, Math. Comp., 61, 1993, 675-699.

P.
Keast and P.H. Muir, *EPDCOL: a more efficient
PDECOL code*, ACM Trans. on Math. Softw., 17, 1991, 153-166. *Reprint
available upon request.*

P.H.
Muir and P.W. Beame, *A note on error expressions for reflected and averaged implicit Runge-Kutta methods*, BIT, 29, 1989, 126-139.

P.H.
Muir and W.H. Enright, *Relationships among some classes of implicit Runge-Kutta
methods and their stability functions*, BIT, 27, 1987, 403-423.

W.H.
Enright and P.H. Muir, *Efficient classes of Runge-Kutta methods for
two-point boundary value problems,* Computing, 37,
1986, 315-334.

**Selected
Technical Reports: **

Paul
Muir and Jack Pew, *Tolerance vs. Error Results for a Class of
Error Control B-spline Gaussian Collocation PDE
Solvers,* Technical Report 2015_001,
Department of Mathematics and Computing Science, Saint Mary's University, 2015.

Jack
Pew, Zhi Li, Paul Muir, *A Computational Study of the
Efficiency of Collocation Software for 1D Parabolic PDEs with
Interpolation-based Spatial Error Estimation,* Technical Report 2013_001, Department of Mathematics
and Computing Science, Saint Mary's University, 2013.

Jason
J. Boisvert, Paul H. Muir, and Raymond J. Spiteri, *A Numerical Study of Global Error and Defect
Control Schemes for BVODE,* Technical
Report 2012_001, Department of
Mathematics and Computing Science, Saint Mary's University, 2012.

T.
Arsenault, T. Smith, P.H. Muir, P.Keast, *Efficient
Interpolation-based Error Estimation for 1D Time-Dependent PDE Collocation
Codes*, Technical Report 2011_001,
Department of Mathematics and Computing Science, Saint Mary's University, 2011.

J.J.
Boisvert, P.H. Muir and R.J. Spiteri**, ***A Numerical Study of Global Error Estimation Schemes for Defect Control
BVODE Codes**, *Technical Report
2009_002, Department of
Mathematics and Computing Science, Saint Mary's University, 2009.

L.F. Shampine, P.H. Muir, H. Xu, *A user-friendly Fortran BVP solver**,* Technical Report 2005_014,
Department of Mathematics and Computing Science, Saint Mary's University, 2005.

R. Wang, P. Keast, P.H.
Muir, *Collocation software
based on a Runge-Kutta time integrator for 1-D **Parabolic PDEs and Schrodinger type problems, with
spatial and temporal error control**,* Technical Report 2005_003,*
*Saint Marys* *University,
Department of Mathematics and Computing Science, 2005.

P.H. Muir, R.N. Pancer, and K.R. Jackson, *Runge-Kutta** software
for the parallel solution of boundary value ODEs*, Technical Report
2000_008, Department of Mathematics and Computing Science, Saint Mary's
University, 2003.

P.H.
Muir and M. Adams, *Mono-implicit Runge-Kutta-Nystrom
methods for boundary value ordinary differential equations*, Technical
Report 2000_003, Department of Mathematics and Computing Science, Saint Mary's
University, 2000.

W.H.
Enright and P.H. Muir, *Superconvergent**
interpolants for discrete collocation solutions*,
Technical Report, Department of Computer Science, University of Toronto,
(1997).

W.H.
Enright and P.H. Muir, *A**
Runge-Kutta type boundary value ODE solver with
defect control**,* Technical Report No. 267/93, Department of
Computer Science,

P.H. Muir and B. Owren, *Order barriers
and characterizations for continuous mono-implicit Runge-Kutta
schemes*, Technical Report No. 258/91, Department of Computer Science,
University of Toronto, (1991).

P.H.
Muir and P. Keast, (1987), *EPDCOL: A more
efficient PDECOL code*, Technical Report 1987CS-6, Computing Science
Division, Department of Mathematics, Statistics, and Computing Science,
Dalhousie University.

**Software:
**

J. Pew, Z. Li, P.H. Muir, *Algorithm** 962: BACOLI: B-spline
Adaptive Collocation Software for PDEs with Interpolation-based Spatial Error
Control*, ACM Trans. on Math. Softw., 42, 3, Article 25, 2016.

J. Pew, P.H. Muir, J. Wang, T. Frasier,
related: an R package for analysing pairwise relatedness from codominant
molecular markers, http://frasierlab.wordpress.com/software/, 2014.

J.J. Boisvert, P.H.
Muir and R.J. Spiteri, BVP_SOLVER-2, Fortran 90/95
Software for the Numerical Solution of Boundary Value Ordinary Differential
Equations with Defect and Global Error Control,
http://cs.stmarys.ca/~muir/BVP_SOLVER_Webpage.shtml, 2012.

J. Pew, P.H. Muir, Z. Li, BACOLI: Collocation
software for 1D Parabolic PDEs with Interpolation-based Error Estimation, 2012.

J. Salvatier, P.H.
Muir, *A Python Wrapper for BVP_SOLVER*,
http://packages.python.org/scikits.bvp_solver/index.html, 2009

R.
Wang, P. Keast, P.H. Muir, *Algorithm** 874: BACOLR - Spatial and Temporal Error Control Software for PDEs
based on High Order Adaptive Collocation*, ACM Trans. Math. Softw.,
34, Article No. 15, 2008. BACOLR:
http://www.mscs.dal.ca/~keast/research/bacolr.html

L.F.
Shampine, P.H. Muir, H. Xu,
*BVP_SOLVER*, Fortran 90/95 based
software for the numerical solution of boundary value ordinary differential
equations, 2006. BVP_SOLVER:
cs.stmarys.ca/~muir/BVP_SOLVER_Webpage.shtml.

R. Wang,
P. Keast, P.H. Muir, *BACOLR*, Collocation* *software
for 1D Parabolic PDEs with spatial and temporal error control based on a Runge-Kutta time integrator, 2004.

R. Wang,
P. Keast, P.H. Muir, *BACOL*, B-spline
Adaptive Collocation software for the numerical solution of systems of
one-dimensional parabolic partial differential equations, 2003.

P.H. Muir, R.N. Pancer, and K.R. Jackson, *PMIRKDC*, Fortran
subroutines for solving boundary value ordinary differential equations on a
parallel shared-memory computer, 2003.

A.M.
Hynick, P. Keast, and P.H.
Muir, *PDODE*, Software for Pulse Detection
in Initial Value ODEs, 2002.

W.H.
Enright and P.H. Muir, "*MIRKDC*",
software for the solution of boundary value ordinary differential equations
using Runge-Kutta methods and defect control, 1996. *MIRKDC
Documentation*

P.
Keast and P.H. Muir, "*EPDCOL*",
software for the solution of partial differential equations using the
collocation in a method-of-lines framework. Algorithm 688 of
the collected algorithms of the Association for Computing Machinery, 1991.

*Saint Mary's
University*** ** Department of Mathematics and Computing Science

Last updated May 9, 2016: Paul Muir (muir@stmarys.ca)