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Robert D Skeel

Publications listed in MathSciNet

[1] Robert D. Engle, Robert D. Skeel, and Matthew Drees. Monitoring energy drift with shadow Hamiltonians. J. Comput. Phys., 206(2):432-452, 2005.
[2] Gang Zou and Robert D. Skeel. Robust variance reduction for random walk methods. SIAM J. Sci. Comput., 25(6):1964-1981 (electronic), 2004.
[3] Qun Ma, Jesús A. Izaguirre, and Robert D. Skeel. Verlet-I/r-RESPA/Impulse is limited by nonlinear instabilities. SIAM J. Sci. Comput., 24(6):1951-1973 (electronic), 2003.
[4] Robert D. Skeel and David J. Hardy. Practical construction of modified Hamiltonians. SIAM J. Sci. Comput., 23(4):1172-1188 (electronic), 2001.
[5] Robert D. Skeel and K. Srinivas. Nonlinear stability analysis of area-preserving integrators. SIAM J. Numer. Anal., 38(1):129-148 (electronic), 2000.
[6] Peter Deuflhard, Jan Hermans, Benedict Leimkuhler, Alan E. Mark, Sebastian Reich, and Robert D. Skeel, editors. Computational molecular dynamics: challenges, methods, ideas, volume 4 of Lecture Notes in Computational Science and Engineering, Berlin, 1999. Springer-Verlag.
[7] Robert D. Skeel. Integration schemes for molecular dynamics and related applications. In The graduate student's guide to numerical analysis '98 (Leicester), volume 26 of Springer Ser. Comput. Math., pages 119-176. Springer, Berlin, 1999.
[8] Tamar Schlick, Robert D. Skeel, Axel T. Brunger, Laxmikant V. Kalé, John A. Board, Jr., Jan Hermans, and Klaus Schulten. Algorithmic challenges in computational molecular biophysics. J. Comput. Phys., 151(1):9-48, 1999. Computational molecular biophysics.
[9] David J. Hardy, Daniel I. Okunbor, and Robert D. Skeel. Symplectic variable step size integration for N-body problems. In Proceedings of the NSF/CBMS Regional Conference on Numerical Analysis of Hamiltonian Differential Equations (Golden, CO, 1997), volume 29, pages 19-30, 1999.
[10] Robert D. Skeel. Symplectic integration with floating-point arithmetic and other approximations. In Proceedings of the NSF/CBMS Regional Conference on Numerical Analysis of Hamiltonian Differential Equations (Golden, CO, 1997), volume 29, pages 3-18, 1999.
[11] B. García-Archilla, J. M. Sanz-Serna, and R. D. Skeel. Long-time-step methods for oscillatory differential equations. SIAM J. Sci. Comput., 20(3):930-963 (electronic), 1999.
[12] Robert D. Skeel. Comments on: “Numerical instability due to varying time steps in explicit wave propagation and mechanics calculations” [J. Comput. Phys. 140 (1998), no. 2, 421-431; MR1616142 (98m:65155)] by J. P. Wright. J. Comput. Phys., 145(2):758-759, 1998.
[13] B. García-Archilla, J. M. Sanz-Serna, and R. D. Skeel. Long-time step methods for oscillatory differential equations. In Numerical analysis 1997 (Dundee), volume 380 of Pitman Res. Notes Math. Ser., pages 111-123. Longman, Harlow, 1998.
[14] Tamar Schlick, Margaret Mandziuk, Robert D. Skeel, and K. Srinivas. Nonlinear resonance artifacts in molecular dynamics simulations. J. Comput. Phys., 140(1):1-29, 1998.
[15] Meiqing Zhang and Robert D. Skeel. Cheap implicit symplectic integrators. Appl. Numer. Math., 25(2-3):297-302, 1997. Special issue on time integration (Amsterdam, 1996).
[16] Todd R. Littell, Robert D. Skeel, and Meiqing Zhang. Error analysis of symplectic multiple time stepping. SIAM J. Numer. Anal., 34(5):1792-1807, 1997.
[17] M. A. López-Marcos, J. M. Sanz-Serna, and Robert D. Skeel. Explicit symplectic integrators using Hessian-vector products. SIAM J. Sci. Comput., 18(1):223-238, 1997. Dedicated to C. William Gear on the occasion of his 60th birthday.
[18] Robert D. Skeel, Guihua Zhang, and Tamar Schlick. A family of symplectic integrators: stability, accuracy, and molecular dynamics applications. SIAM J. Sci. Comput., 18(1):203-222, 1997. Dedicated to C. William Gear on the occasion of his 60th birthday.
[19] Robert D. Skeel, editor. {Dedicated to C. William Gear on the occasion of his 60th birthday}. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1997. Including papers from the International Conference on Scientific Computation and Differential Equations (SciCADE 95) held at Stanford University, Stanford, CA, 1995, SIAM J. Sci. Comput. 18 (1997), no. 1.
[20] M. A. Lopez-Marcos, J. M. Sanz-Serna, and Robert D. Skeel. An explicit symplectic integrator with maximal stability interval. In Numerical analysis, pages 163-175. World Sci. Publ., River Edge, NJ, 1996.
[21] Benedict J. Leimkuhler, Sebastian Reich, and Robert D. Skeel. Integration methods for molecular dynamics. In Mathematical approaches to biomolecular structure and dynamics (Minneapolis, MN, 1994), volume 82 of IMA Vol. Math. Appl., pages 161-185. Springer, New York, 1996.
[22] M. A. López-Marcos, J. M. Sanz-Serna, and R. D. Skeel. Cheap enhancement of symplectic integrators. In Numerical analysis 1995 (Dundee, 1995), volume 344 of Pitman Res. Notes Math. Ser., pages 107-122. Longman, Harlow, 1996.
[23] Robert D. Skeel and Jeffrey J. Biesiadecki. Symplectic integration with variable stepsize. Ann. Numer. Math., 1(1-4):191-198, 1994. Scientific computation and differential equations (Auckland, 1993).
[24] Daniel I. Okunbor and Robert D. Skeel. Canonical Runge-Kutta-Nyström methods of orders five and six. J. Comput. Appl. Math., 51(3):375-382, 1994.
[25] Benedict J. Leimkuhler and Robert D. Skeel. Symplectic numerical integrators in constrained Hamiltonian systems. J. Comput. Phys., 112(1):117-125, 1994.
[26] Robert D. Skeel. Variable step size destabilizes the Störmer/leapfrog/Verlet method. BIT, 33(1):172-175, 1993.
[27] Jeffrey J. Biesiadecki and Robert D. Skeel. Dangers of multiple time step methods. J. Comput. Phys., 109(2):318-328, 1993.
[28] Hon-Wah Tam and Robert D. Skeel. Stability of parallel explicit ODE methods. SIAM J. Numer. Anal., 30(4):1179-1192, 1993.
[29] Robert D. Skeel and Hon-Wah Tam. Potential for parallelism in explicit linear methods. In Computational ordinary differential equations (London, 1989), volume 39 of Inst. Math. Appl. Conf. Ser. New Ser., pages 377-383. Oxford Univ. Press, New York, 1992.
[30] Robert D. Skeel and C. W. Gear. Does variable step size ruin a symplectic integrator? Phys. D, 60(1-4):311-313, 1992. Experimental mathematics: computational issues in nonlinear science (Los Alamos, NM, 1991).
[31] Robert D. Skeel and Hon-Wah Tam. Limits of parallelism in explicit ODE methods. Numer. Algorithms, 2(3-4):337-349, 1992.
[32] Daniel Okunbor and Robert D. Skeel. An explicit Runge-Kutta-Nyström method is canonical if and only if its adjoint is explicit. SIAM J. Numer. Anal., 29(2):521-527, 1992.
[33] Ren Li Guo and Robert D. Skeel. An algebraic hierarchical basis preconditioner. Appl. Numer. Math., 9(1):21-32, 1992.
[34] Daniel Okunbor and Robert D. Skeel. Explicit canonical methods for Hamiltonian systems. Math. Comp., 59(200):439-455, 1992.
[35] M. A. López Marcos, J. M. Sanz Serna, and Robert D. Skeel. Some problems of molecular dynamics. In XIV CEDYA/IV Congress of Applied Mathematics (Spanish)(Vic, 1995), page 8 pp. (electronic). Univ. Barcelona, Barcelona, 199?
[36] C. W. Gear and R. D. Skeel. The development of ODE methods: a symbiosis between hardware and numerical analysis. In A history of scientific computing (Princeton, NJ, 1987), ACM Press Hist. Ser., pages 88-105. ACM, New York, 1990.
[37] Robert D. Skeel and Martin Berzins. A method for the spatial discretization of parabolic equations in one space variable. SIAM J. Sci. Statist. Comput., 11(1):1-32, 1990.
[38] Robert D. Skeel. Waveform iteration and the shifted Picard splitting. SIAM J. Sci. Statist. Comput., 10(4):756-776, 1989.
[39] Robert D. Skeel. Global error estimation and the backward differentiation formulas. Appl. Math. Comput., 31:197-208, 1989. Numerical ordinary differential equations (Albuquerque, NM, 1986).
[40] Robert D. Skeel. The second-order backward differentiation formula is unconditionally zero-stable. Appl. Numer. Math., 5(1-2):145-149, 1989. Recent theoretical results in numerical ordinary differential equations.
[41] Thomas N. Gambill and Robert D. Skeel. Logarithmic reduction of the wrapping effect with application to ordinary differential equations. SIAM J. Numer. Anal., 25(1):153-162, 1988.
[42] R. D. Skeel. Corrigendum: “Equivalent forms of multistep formulas” [Math. Comp.33 (1979), no.148, 1229-1250; MR0537967 (80j:65027)]. Math. Comp., 47(176):769, 1986.
[43] Robert D. Skeel. Construction of variable-stepsize multistep formulas. Math. Comp., 47(176):503-510, S45-S52, 1986.
[44] Robert D. Skeel. The order of accuracy for deferred corrections using uncentered end formulas. SIAM J. Numer. Anal., 23(2):393-402, 1986.
[45] Robert D. Skeel. Thirteen ways to estimate global error. Numer. Math., 48(1):1-20, 1986.
[46] Robert D. Skeel. Computational error estimates for stiff ODEs. In Computational mathematics, I (Benin City, 1983), volume 8 of Boole Press Conf. Ser., pages 3-10. Boole, Dún Laoghaire, 1985.
[47] R. D. Skeel and L. W. Jackson. The stability of variable-stepsize Nordsieck methods. SIAM J. Numer. Anal., 20(4):840-853, 1983.
[48] Robert D. Skeel. A theoretical framework for proving accuracy results for deferred corrections. SIAM J. Numer. Anal., 19(1):171-196, 1982.
[49] Robert D. Skeel. Effect of equilibration on residual size for partial pivoting. SIAM J. Numer. Anal., 18(3):449-454, 1981.
[50] Robert D. Skeel. Iterative refinement implies numerical stability for Gaussian elimination. Math. Comp., 35(151):817-832, 1980.
[51] Robert D. Skeel. Equivalent forms of multistep formulas. Math. Comp., 33(148):1229-1250, 1979.
[52] Robert D. Skeel. Scaling for numerical stability in Gaussian elimination. J. Assoc. Comput. Mach., 26(3):494-526, 1979.
[53] Robert D. Skeel and Antony K. Kong. Blended linear multistep methods. ACM Trans. Math. Software, 3(4):326-345, 1977.
[54] R. D. Skeel and L. W. Jackson. Consistency of Nordsieck methods. SIAM J. Numer. Anal., 14(5):910-924, 1977.
[55] Robert Skeel. Analysis of fixed-stepsize methods. SIAM J. Numer. Anal., 13(5):664-685, 1976.

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