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Volume 10, Issue 1


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Approximating Solutions of Linear Ordinary Differential Equations with Periodic Coefficients by Exact Picard Iterates
Armando G. M. Neves


[1] S. C. Sinha and E. A. Butcher, "Symbolic Computation of Fundamental Solution Matrices for Linear Time-Periodic Dynamical Systems," Journal of Sound and Vibration, 206(1), 1997 pp. 61-85.

[2] E. A. Butcher and S. C. Sinha, "Symbolic Computation of Local Stability and Bifurcation Surfaces for Nonlinear Time-Periodic Systems," Nonlinear Dynamics, 17(1), 1998 pp. 1-21.

[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: Springer-Verlag, 1985.

[5] M. Braun, Differential Equations and Their Applications, 2nd ed., New York: Springer-Verlag, 1978.

[6] A. G. M. Neves, "Symbolic Computation of High-Order Exact Picard Iterates for Systems of Linear Differential Equations with Time-Periodic Coefficients," in Computational Science--ICCS 2003, International Conference, Melbourne, Australia and St. Petersburg, Russia, June 2003, Proceedings, Part 1; Lecture Notes in Computer Science, Vol. 2657, pp. 838-847, Heidelberg: Springer-Verlag, 2003.

[7] D. J. Acheson, "A Pendulum Theorem," Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 443, 1993 pp. 239-245.

[8] D. J. Acheson and T. Mullin, "Upside-down Pendulums," Nature, 366, 1993 pp. 215-216.

[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. 3007-3022.

[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. 390-407.

[11] D. Frenkel and R. Portugal, "Algebraic Methods to Compute Mathieu Functions," Journal of Physics A, Mathematical and General, 34, 2001 pp. 3541-3551.

[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. 447-464.

[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. 1-10.

[16] A. Stephenson, "On Induced Stability," Philosophical Magazine, 15, 1908 pp. 233-236.

[17] H. Goldstein, Classical Mechanics, 2nd ed., Reading, MA: Addison-Wesley, 1980.

[18] D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, 2nd ed., Oxford: Clarendon Press, 1987.

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