Refereed Journal Papers
Software
- 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.
- 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.
- 2006. Sharp P.W., N-body simulations: the performance of some integrators, ACM Trans. Maths. Softw., 32(3), 375-395.
- 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.
- 2002. Sharp P.W., Requirements of a package for N-body simulations of the Solar System, Numerical Algorithms, 31, 271-279.
- 1991. Sharp P.W., Numerical comparison of explicit Runge-Kutta pairs of orders four through eight, TOMS, 17, 387-409.
Algorithms
- 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-.
- 2013. Grazier K.R., Newman W.I., Sharp P.W., A multirate Störmer algorithm for close encounters, Astron. J., 145, 112-110.
- 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.
- 2013. Sharp P.W., Qureshi M.A., Grazier K.R., High order explicit Runge-Kutta Nyström pairs, Num. Alg., 62(1), 133-148.
- 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.
- 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).
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 1998. Sharp P.W., Verner J.H., Generation of high-order interpolants for explicit Runge-Kutta pairs, TOMS, 24, 1, 13-29.
- 1998. Sharp P.W., Parsons L., The efficiency of extended explicit Pouzet Volterra Runge-Kutta pairs, New Zealand Journal of Mathematics, 27, 97-111.
- 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.
- 1994. Burrage K., Sharp P.W., A class of variable-step explicit Nordsieck multistep methods, SIAM J. Num. Anal., 31, 1434-1451.
- 1994. Verner J.H., Sharp P.W., Completely imbedded Runge-Kutta formula pairs, SIAM J. Num. Anal., 31, 1169-1190.
- 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.
- 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.
- 1992. Sharp P.W., Fine J.M., A contrast of direct and transformed Nystrom pairs, J. Comp. and Appl. Math., 42, 293-308.
- 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
- 2014. Grazier K.R., Castillo-Rogez J.C., Sharp P.W., Dynamical delivery of volatiles to the outer main belt, Icarus, 232, 13-21.
- 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.
- 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.
- 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.
- 1985. Spence D.A., Sharp P.W., Self-Similar solutions for elastohydrodynamic cavity flow, Proc. R. Soc. Lond. A 400, 289-313.
- 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
- 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.
- 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.
- 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
- 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
- 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.
- 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.
- Sharp P.W., A collection of restricted three-body test problems Report Series 460, Department of Mathematics, University of Auckland, March, 2001.
- 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.
- Sharp P.W., A comparison of explicit Pouzet Runge-Kutta pairs for VIDEs, Mathematical Preprint 1998-1, Queen's University, Canada, 1998.
- Sharp P.W., Verner J.H., RKCHK user guide, Report Series No. 366, Department of Mathematics, University of Auckland, 1996.
- 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.
- 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.
- Sharp P.W., User guide for BEL4, Report Series No. 347, Department of Mathematics, University of Auckland, 1996.
- 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.
- 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.
- 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.
- 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
- Sharp P.W., Verner J.H., Explicit Runge-Kutta 4-5 pairs with interpolants, Mathematical Preprint No. 1995-03, Queen's University, 1995.
- 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.
- Sharp P.W., New low order Runge-Kutta pairs, TR 222/89, Department of Computer Science, University of Toronto, 1989.
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