References[AB04] M. L. Abell and J. P. Braselton, Differential Equations with Mathematica, 3rd ed., New York: Elsevier Academic Press, 2004. [A89] S. A. Abramov, "Rational solutions of linear differential and difference equations with polynomial coefficients," USSR Comput. Maths. Math. Phys., 29, 1989 pp. 7-12. [A96] S. A. Abramov, "Symbolic search algorithms for partial d'Alembertian solutions of linear equations," Programming and Computer Software, 22(1), 1996 p. 26. [AB01] S. A. Abramov and M. Bronstein, "On solutions of linear functional systems," in Proc. ISSAC'01, pp. 1-6. [AK91] S. A. Abramov and K. Yu. Kvansenko, "Fast algorithms to search for the rational solutions of linear differential equations with polynomial coefficients," Proc. ISSAC'91, pp. 267-270. [AP94] S. A. Abramov and M. Petkovsek, "D'Alembertian solutions of linear differential and difference equations," Proc. ISSAC'94, pp. 169-174. [ABP95] S. A. Abramov, M. Bronstein, and M. Petkovsek, "On polynomial solutions of linear operator equations," Proc. ISSAC'95, pp. 290-296. [B93] A. Bocharov, "Symbolic solvers for nonlinear differential equations," The Mathematica Journal, 3(2), 1993 pp. 63-69. [BD97] W. F. Boyce and R. C. DiPrima, Elementary Differential Equations, New York: John Wiley and Sons, 1997. [BM91] C. B. Boyer and U. C. Merzbach, A History of Mathematics, 2nd ed., New York: John Wiley, 1991. [B91] M. Bronstein, "The Risch differential equation on an algebraic curve," Proc. ISSAC'91, pp. 241-246. [B92] M. Bronstein, "On solutions of linear ordinary differential equations in their coefficient field," J. Symbolic Computation, 13, 1992 pp. 413-439. [B92a] M. Bronstein, "Integration and differential equations in computer algebra," Programming and Computer Software, 18(5), 1992 pp. 201-217. [B92b] M. Bronstein, "Linear ordinary differential equations: breaking through the order 2 barrier," Proc. ISSAC'92, pp. 42-48.
[C80] S. L. Campbell,
Singular Systems of Differential Equations I
, London: Pitman, 1980.
[C82] S. L. Campbell,
Singular Systems of Differential Equations II
, London: Pitman, 1982.
[CC04] L. Chan and E. S. Cheb-Terrab, "Non-Liouvillian solutions for second order linear ODEs," Proc. ISSAC'04, Santander, Spain, pp. 80-86. [CDM97] E. S. Cheb-Terrab, L. G. S. Duarte, and L. A. C. P. da Mota, "Computer algebra solving of first order ODEs using symmetry methods," Comp. Phys. Comm., 101, 1997 p. 254. [CR99] E. S. Cheb-Terrab and A. D. Roche, "Integrating factors for second order ODEs," J. Symbolic Computation, 27, 1999 p. 501. [CR00] E. S. Cheb-Terrab and A. D. Roche, "Abel ODEs: Equivalence and integrable classes," Comp. Phys. Comm., 130, 2000 p. 204. [D58] M. P. Drazin, "Pseudo Inverses in Associative Rays and Semigroups," American Mathematical Monthly, 65, 1958 pp. 506-514. [F59] A. R. Forsyth, Theory of Differential Equations, 6 vols., New York: Dover, 1959. [I99] N. H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, New York: John Wiley & Sons, 1999. [I44] E. L. Ince, Ordinary Differential Equations, New York: Dover, 1944. [K59] E. Kamke, Differentialgleichungen: Losungsmethoden und Losungen, Leipzig: Akademische Verlagsgesellschaft, 1959. [K74] E. Kamke, Differentialgleichungen Losungsmethoden und Losungen, Bd. II: Partielle differentialgleichungen, New York: Chelsea Publishing Co., 1974. [K00] J. Kevorkian, Partial Differential Equations: Analytical Solution Techniques, New York: Springer-Verlag, 2000. [K72] M. Kline, Mathematical Thought from Ancient to Modern Times, Vol. 2, New York: Oxford University Press, 1972. [K86] J. J. Kovacic, "An algorithm for solving second order linear homogeneous differential equations," J. Symbolic Computation, 2, 1986 pp. 3-43. [L01] J. J. Kovacic, "An algorithm for solving second order linear homogeneous differential equations," Lecture, City College of New York, 2001. [KPS03] P. K. Kythe, P. Puri, and M. R. Schäferkotter, Partial Differential Equations and Boundary Value Problems with Mathematica, 2nd ed., Boca Raton, FL: Chapman and Hall/CRC, 2003. [L65] N. N. Lebedev, Special Functions and Their Applications, Englewood-Cliffs, NJ: Prentice-Hall, 1965.
[M00] C. D. Meyer,
Matrix Analysis and Applied Linear Algebra
, Philadelphia: SIAM, 2000.
[M60] G. M. Murphy, Ordinary Differential Equations and Their Solutions, New York: Van Nostrand, 1960. [M47] N. W. McLachlan, Theory and Application of Mathieu Functions, Oxford: Oxford University Press, 1947. [O95] P. J. Olver, Equivalence, Invariants and Symmetry, Cambridge: Cambridge University Press, 1995. [PZ95] A. D. Polynanin and V. F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, Boca Raton, FL: CRC Press, 1995. [S81] B. D. Saunders, "An Implementation of Kovacic's Algorithm for Solving Second Order Linear Homogeneous Differential Equations," in Proc. SYMSAC'81 (P. Wang, ed.), New York: ACM, p. 105. [S85] L. Schlesinger, Handbuch der Theorie der linearen differentialgleichungen, Leipzig: Teubner, 1985. [SS98] M. Shirvani and J. W.-H. So, "Solutions of linear differential algebraic equations," SIAM Review, 40(2), 1998 pp. 344-346. [S57] I. Sneddon, Elements of Partial Differential Equations, Singapore: McGraw-Hill, 1957. [T05] M. Trott, The Mathematica GuideBook for Symbolics, Berlin: Springer-Verlag, 2005. [UW96] F. Ulmer and J-A. Weil, "Note on Kovacic's algorithm," J. Symbolic Computation, 22, 1996. pp. 179-200. [WW27] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge: Cambridge University Press, 1927. [W02] S. Wolfram, A New Kind of Science, Champaign: Wolfram Media, Inc., 2002. [W04] S. Wolfram, The Mathematica Book, 5th ed., Champaign: Wolfram Media, Inc., 2004. [Z89] D. Zwillinger, Handbook of Differential Equations, San Diego: Academic Press, 1989.
|
