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Approximating Solutions of Linear Ordinary Differential Equations with Periodic Coefficients by Exact Picard Iterates
References[1] S. C. Sinha and E. A. Butcher, "Symbolic Computation of Fundamental Solution Matrices for Linear TimePeriodic Dynamical Systems," Journal of Sound and Vibration, 206(1), 1997 pp. 6185. [2] E. A. Butcher and S. C. Sinha, "Symbolic Computation of Local Stability and Bifurcation Surfaces for Nonlinear TimePeriodic Systems," Nonlinear Dynamics, 17(1), 1998 pp. 121. [3] A. H. Nayfeh, Perturbation Methods, New York: John Wiley & Sons, 1973. [4] J. A. Sanders and F. Verhulst, Averaging Methods in Nonlinear Dynamical Systems, New York: SpringerVerlag, 1985. [5] M. Braun, Differential Equations and Their Applications, 2nd ed., New York: SpringerVerlag, 1978. [6] A. G. M. Neves, "Symbolic Computation of HighOrder Exact Picard Iterates for Systems of Linear Differential Equations with TimePeriodic Coefficients," in Computational ScienceICCS 2003, International Conference, Melbourne, Australia and St. Petersburg, Russia, June 2003, Proceedings, Part 1; Lecture Notes in Computer Science, Vol. 2657, pp. 838847, Heidelberg: SpringerVerlag, 2003. [7] D. J. Acheson, "A Pendulum Theorem," Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 443, 1993 pp. 239245. [8] D. J. Acheson and T. Mullin, "Upsidedown Pendulums," Nature, 366, 1993 pp. 215216. [9] M. V. Bartuccelli, G. Gentile, and K. V. Georgiou, "On the Dynamics of a Vertically Driven Damped Planar Pendulum," Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 457, 2001 pp. 30073022. [10] F. A. Alhargan, "Algorithms for the Computation of All Mathieu Functions of Integer Orders," ACM Transactions on Mathematical Software (TOMS), 26(3), 2000 pp. 390407. [11] D. Frenkel and R. Portugal, "Algebraic Methods to Compute Mathieu Functions," Journal of Physics A, Mathematical and General, 34, 2001 pp. 35413551. [12] A. G. M. Neves, "Upper and Lower Bounds on Mathieu Characteristic Numbers of Integer Orders," Communications on Pure and Applied Analysis, 3(3), 2004 pp. 447464. [13] R. E. Maeder, The Mathematica Programmer, Boston: AP Professional, 1994. [14] S. Wolfram, The Mathematica Book, 4th edition, Champaign, Oxford: Wolfram Media/Cambridge University Press, 1999. [15] A. Stephenson, "On a New Type of Dynamical Stability," Memoirs and Proceedings of the Manchester Literary and Philosophical Society, 52(8), 1908 pp. 110. [16] A. Stephenson, "On Induced Stability," Philosophical Magazine, 15, 1908 pp. 233236. [17] H. Goldstein, Classical Mechanics, 2nd ed., Reading, MA: AddisonWesley, 1980. [18] D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, 2nd ed., Oxford: Clarendon Press, 1987.


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