Research: Paul Muir

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, 201—217.

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 Mary’s 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, University of Toronto, (1993).

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, 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

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)