Selected Publications:

R. Wang,  P. Keast, P.H. Muir, Algorithm 874: BACOLR: Spatial and Temporal Error Control Software for PDEs based on High Order Adaptive Collocation, to appear in Trans. on Math. Soft., 34, 2008.

L.F. Shampine, P.H. Muir, H. Xu, A user-friendly Fortran BVP 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. Online Appendix.

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.

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 iniInitial 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.

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

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.

W.H. Enright and P.H. Muir, Superconvergent interpolants for discrete collocation solutions, SIAM J. Sci. Comp., 21, (1999), 227-254.

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.

T.B. Nokonechny, P. Keast, and P.H. Muir, (1996), 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, pp. 207-223. Available upon request.

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.

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

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. Available upon request.

K. Burrage, F.H. Chipman, P.H. Muir, Order results for mono-implicit Runge-Kutta methods, SIAM J. Numer. Anal., 31, (1994), 876-891.

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

P.H. Muir and P. Keast, EPDCOL: a more efficient PDECOL code, ACM Trans. on Math. Softw., 17, (1991), 153-166.

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. Available upon request.

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. Available upon request.

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

 

Selected Technical Reports:

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 2000-08, Department of Mathematics and Computing Science, Saint Mary's University, 2003. See Department of Mathematics and Computing Science, Saint Mary's University, Technical Report Page.

P.H. Muir and M. Adams, Mono-implicit Runge-Kutta-Nystrom methods for boundary value ordinary differential equations, Technical Report 2000-03, Department of Mathematics and Computing Science, Saint Mary's University, 2000. See Department of Mathematics and Computing Science, Saint Mary's University, Technical Report Page.

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. Available upon request.

 

Software:

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.

 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 Apr. 18, 2008: Paul Muir ( muir@stmarys.ca)