Philip W.Sharp

List of research publications

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Table of contents

Refereed Journal Papers

Software

  1. 2016. Sharp P.W., Newman W.I., GPU-enabled N-body simulations of the Solar System using a VOVS Adams integrator, J. of Comp. Sci., 16, 89-97.
  2. 2012. Sharp P.W., Castillo-Rogez J.C., Grazier, K.R., The performance of phase-lag enhanced explicit Runge-Kutta Nyström pairs on N-body problems, J. Comput. Appl. Maths., 236(9), 2378-2386.
  3. 2006. Sharp P.W., N-body simulations: the performance of some integrators, ACM Trans. Maths. Softw., 32(3), 375-395.
  4. 2004. Sharp P.W., Comparisons of integrators on a diverse colleciton of restricted three-body test problems, IMA J. of Num. Anal. 24, 557-575.
  5. 2002. Sharp P.W., Requirements of a package for N-body simulations of the Solar System, Numerical Algorithms, 31, 271-279.
  6. 1991. Sharp P.W., Numerical comparison of explicit Runge-Kutta pairs of orders four through eight, TOMS, 17, 387-409.
Algorithms
  1. 2016. Sharp P.W., Newman W.I., A multirate variable-timestep algorithm for n-body solar system simulations with collisions, Astron. J., 151 (3), 64-.
  2. 2013. Grazier K.R., Newman W.I., Sharp P.W., A multirate Störmer algorithm for close encounters, Astron. J., 145, 112-110.
  3. 2013. Nguyen-Ba T., Desjardins S.J., Sharp P.W., Vaillancourt R., Contractivity-preserving explicit Hermite-Obrechkoff ODE solver of order 13, Celest. Mech. Dyn. Astr., 117(4), 423-434.
  4. 2013. Sharp P.W., Qureshi M.A., Grazier K.R., High order explicit Runge-Kutta Nyström pairs, Num. Alg., 62(1), 133-148.
  5. 2008. Nguyen-Ba T., Sharp P.W., Vaillancourt R., Hermite-Birkhoff-Obrechkoff four-stage four-step ODE solver of order 14 with quantized stepsize, J. Comput. Appl. Maths., 222(2), 608-621.
  6. 2007. Nguyen-Ba T., Sharp, P.W., Yagoub H., Vaillancourt R., Hermite-Birkhoff-Obrechkoff 3-stage 4-step ODE solver of order 14 with quantized stepsize, Canadian Applied Mathematics Quarterly, 15(2).
  7. 2006. Sharp P.W., Vaillancourt, R., Explicit Pouzet Runge-Kutta pairs for Volterra integro differential equations, Scientific Proceedings of Riga Technical University, Boundary Field Problems and Computer Simulation, 29(48), 95-104.
  8. 2006. Sharp P.W., Vaillancourt, R., New Nystrom pairs for the general second-order problem. Scientific Proceedings of Riga Technical University, Boundary Field Problems and Computer Simulation, 29(48), 15-24.
  9. 2005. Sharp P.W., Vaillancourt, R., Error growth of some symplectic explicit Runge-Kutta Nystrom methods for a simulation of the gas giants, Scientific Proceedings of Riga Technical University, Computer Science Series, 25(47), 32-38.
  10. 2005. Sharp P.W., Vaillancourt R., Efficient order five second-derivative explicit Runge-Kutta pairs with interpolants, Scientific Proceedings of Riga Technical University, Computer Science Series, 25(47), 39-47.
  11. 2000. Chou Lin-Yi, Sharp P.W., Order 5 symplectic explicit Runge-Kutta Nystrom methods, Journal of Applied Mathematics and Decision Sciences 4, 2, 143-150.
  12. 2000. Sharp P.W., Verner J.H., Some extended explicit Bel'tyukov pairs for Volterra integral equations of the second kind, SIAM J. Num. 38, 2, 347-359.
  13. 2000. Sharp P.W., Verner J.H, Extended explicit Bel'tyukov pairs of orders 4 and 5 for Volterra integral equations of the second kind, App. Num. Math. 34, 2, 261-274.
  14. 2000. Sharp P.W., High order explicit Runge-Kutta pairs for ephemerides of the Solar System and the Moon, Journal of Applied Mathematics and Decision Sciences 4, 2 183-192.
  15. 1998. Sharp P.W., Verner J.H., Generation of high-order interpolants for explicit Runge-Kutta pairs, TOMS, 24, 1, 13-29.
  16. 1998. Sharp P.W., Parsons L., The efficiency of extended explicit Pouzet Volterra Runge-Kutta pairs, New Zealand Journal of Mathematics, 27, 97-111.
  17. 1994. Malek F., Sharp P.W., Vaillancourt R., Minimum number of stages for low-order explicit Runge-Kutta Nystrom pairs, C.R. Math. Rep. Acad. Sci. Canada, XVI, 79-84.
  18. 1994. Burrage K., Sharp P.W., A class of variable-step explicit Nordsieck multistep methods, SIAM J. Num. Anal., 31, 1434-1451.
  19. 1994. Verner J.H., Sharp P.W., Completely imbedded Runge-Kutta formula pairs, SIAM J. Num. Anal., 31, 1169-1190.
  20. 1993. Sharp P.W., Smart E., Explicit Runge-Kutta pairs with one more stage than the minimum possible, SIAM J. Sci. Comput, 42, 338-348.
  21. 1992. Sharp P.W., Fine J.M., Some Nystrom pairs for the general second order initial value problem, J. Comp. and Appl. Math.,42, 279-291.
  22. 1992. Sharp P.W., Fine J.M., A contrast of direct and transformed Nystrom pairs, J. Comp. and Appl. Math., 42, 293-308.
  23. 1990. Sharp P.W., Fine J.M., Burrage K., Two-stage and three-stage diagonally implicit Runge-Kutta Nystrom methods of orders three and four , IMA J. Num. Anal, 10, 489-504.
Modelling
  1. 2014. Grazier K.R., Castillo-Rogez J.C., Sharp P.W., Dynamical delivery of volatiles to the outer main belt, Icarus, 232, 13-21.
  2. 1998. Balanathan R., Pahalawaththa N.C.,Annakkage U.D., Sharp P.W., Undervoltage load shedding to avoid voltage instability, IEE Proc.-Gener. Transm. Distrib., 145, 2, 175-180.
  3. 1989. Spence D.A., Sharp P.W., Distortion and necking of a viscous inclusion in Stokes flow, Proc. R. Soc. Lond. A 422, 173-192.
  4. 1987. Spence D.A., Sharp P.W., Turcotte D.L., Buoyancy driven crack propagation: a mechanism for magma migration, J. Fluid Mech.,174, 135-153, 1987.
  5. 1985. Spence D.A., Sharp P.W., Self-Similar solutions for elastohydrodynamic cavity flow, Proc. R. Soc. Lond. A 400, 289-313.
  6. 1984. Sharp P.W., Unsteady waves on an open two layer fluid, J. Austral. Math. Soc. Ser. B, 26, 183-199.

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Referred Conference Proceedings

Algorithms
  1. Grazier K.R., Newman W.I., Hyman J.M., Sharp P.W., Long simulations of the Solar System: Brouwer's Law and chaos, ANZIAM J. (electronic supplement) 46 (2005), C1086-C1103.
  2. Grazier K.R., Newman W.I., Hyman J.M., Sharp P.W., Goldstein D.J., Achieving Brouwer's Law with high-order Stormer multistep methods, ANZIAM J. (electronic supplement) 46 (2005), C786-C804.
  3. Burrage K., Sharp P.W., A family of Nordsieck methods, Computational ordinary differential equations (London, 1989) , Inst. Math. Appl. Conf. Ser. New Ser., 39 (1992), 47-60 , Oxford Univ. Press, New York.
Modelling
  1. Rahman S., Sharp P.W., A numerical study of a traffic flow problem, proceedings of the Fifth Annual Paper Meet, Institution of Engineers, held November 1998, Chittagong, Bangladesh, 434 - 442.

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Departmental technical reports and preprints

All the reports and preprints listed below differ significantly from the refereed papers listed above.

Software and test problems

  1. Sharp P.W., Krogh F., DDAE: an integrator for ODEs, DDEs and DAEs, part I, Report series 480, Department of Mathematics, University of Auckland, July 2002.
  2. Sharp P.W., Long initial value test problems from simulations of the Solar Sytem, Report Series 468, Department of Mathematics, University of Auckland, July 2001.
  3. Sharp P.W., A collection of restricted three-body test problems Report Series 460, Department of Mathematics, University of Auckland, March, 2001.
  4. Sharp P.W., Comparisons of high order Stormer and explicit Runge-Kutta methods for N-body simulations of the solar system, Report Series 449, Department of Mathematics, University of Auckland, June, 2000.
  5. Sharp P.W., A comparison of explicit Pouzet Runge-Kutta pairs for VIDEs, Mathematical Preprint 1998-1, Queen's University, Canada, 1998.
  6. Sharp P.W., Verner J.H., RKCHK user guide, Report Series No. 366, Department of Mathematics, University of Auckland, 1996.
  7. Sharp P.W., Verner J.H., Dual precision software for checking explicit Runge-Kutta methods, Report Series No. 363, Department of Mathematics, University of Auckland, 1996.
  8. Sharp P.W., BEL4: an explicit Bel'tyukov integrator for Volterra integral equations of the second kind, Report Series No. 348, Department of Mathematics, University of Auckland, 1996.
  9. Sharp P.W., User guide for BEL4, Report Series No. 347, Department of Mathematics, University of Auckland, 1996.
  10. Sharp P.W., Butcher J.C., Comparison of some Runge-Kutta integrators for delay differential equations, Report Series No. 309, Department of Mathematics, University of Auckland, 1994.
  11. Sharp P.W., Fine J.M., User-guide for ERNY - an explicit Runge-Kutta Nystrom integrator for second order initial value problems, TR 198/87, Department of Computer Science, University of Toronto, 1987.
  12. Sharp P.W., Fine J.M., ERNY - an integrator for second order initial value problems, TR 199/87, Department of Computer Science, University of Toronto, 1987.
  13. Sharp P.W., The vectorization of low order explicit Runge-Kutta Nystrom pairs on a CRAY X-MP/22, TR 203/87, Department of Computer Science, University of Toronto, 1987.
Algorithms
  1. Sharp P.W., Verner J.H., Explicit Runge-Kutta 4-5 pairs with interpolants, Mathematical Preprint No. 1995-03, Queen's University, 1995.
  2. Enright W.H., Higham D.J., Owren B., Sharp P.W., A survey of the explicit Runge- Kutta method, TR 291/94, Department of Computer Science, University of Toronto, 1994.
  3. Sharp P.W., New low order Runge-Kutta pairs, TR 222/89, Department of Computer Science, University of Toronto, 1989.

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