Bibliography on Differential Equations

• [AG] Agnew, R.P. Differential Equations, 2nd ed., McGraw-Hill, New York, 1960.
• [BB] Bernoff, A.J., and Bertozzi, A. L, Singularities in a modified Kuramoto-Sivashinsky equation describing interface motion for phase transition, Physica D 85 (1995), 375–404.
• [BH] Briggs, W. L., and Henson, V. E., The DFT: An Owner’s Manual for the Discrete Fourier Transform, SIAM, Philadelphia, PA, 1995.
• [BL] Bieberbach, L., Differentialgleichungen, 2nd ed., Springer, Berlin, 1965.
• [BR] Birkhoff, G and Rota, G. Ordinary Differential Equations, Blaisdell, New York, 1962.
• [BJ] Butcher, J., Numerical Methods for Ordinary Differential Equations, Second Edition, Wiley, Hoboken, NJ, 2008.
• [CP] Cartwright, J. H. E., and Piro, O., The Dynamics of Runge–Kutta Methods, Int. J. Bifurcation and Chaos 2 (1992), 427–449..
• [CS] Channell, P. J., and Scovel, C., Symplectic integration of Hamiltonian systems, Nonlinearity 3 (1990), 231.
• [CFL] Courant, R., Friedrichs, K., and Lewy, H., On the partial difference equations of mathematical physics, IBM Journal, March 1967, pp. 215–234, English translation of the 1928 German original, Mathematische Annalen 100 (1928), 32–74.
• [DR] Devaney, R., First Course in Chaotic Dynamical System: Theory and Experiment, Westview Press, Reading, MA, 1992.
• [DK] Devaney, R., and Keen, L., Editors, Chaos and Fractals: The Mathematics Behind the Computer Graphics, American Mathematical Society, Providence, RI, 1989.
• [EWH] Enright, W. H., Continuous numerical methods for ODEs with defect control, Journal of Computational and Applied Mathematics 125 (2000), n. 1-2, 159–170.
• [FB] Fornberg, B., Practical Guide to Pseudospectral Methods, Cambridge University Press, New York, NY, 1996.
• [FP] Friedlander, S., and Pavlovi´c, S., Blowup in a three-dimensional vector model for the Euler equations, Comm. Pure Appl. Math. 57 (6) (2004), 705–725.
• [GCW] Gear, C. W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice Hall, Englewood Cliffs, NJ, 1971.
• [GS] Gill, S., A process for the step-by-step integration of differential equations in an automatic computing machine, Proc. Cambridge Philos. Soc. 47 (1951), 96–108.
• [GJ] Gleick, J., Chaos: Making a New Science, Penguin, London, 2008.
• [GH] Goldstein, H., Classical Mechanics, Addison Wesley, San Francisco, 2002.
• [GBL] Gowers, T., Barrow-Green, J., and Leader, I., Editors, The Princeton Companion to Mathematics, Princeton University Press, Princeton, NJ, 2008.
• [HLW] Hairer, E., Lubich, C., and Wanner, G., Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, Springer Series in Comput. Mathematics, Vol. 31, Springer-Verlag, 2002.
• [HP] Henrici, P., Discrete Variable Methods in Ordinary Differential Equations, John Wiley & Sons, New York, NY, 1962.
• [HDJ] Higham, D. J., Robust defect control with Runge-Kutta schemes, SIAM Journal on Numerical Analysis 26 (1989) n. 5, 1175–1183.
• [HS] Hirsch, M. W., and Smale, S., Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, New York, 1960.
• [HW] Hubbard, J., and West, B., Differential Equations, Dynamical Systems, and Linear Algebra, Springer, New York, 1991.
• [IK] Isaacson, E., and Keller, H. B., Analysis of Numerical Methods, Reprint of 1966 Edition, Dover, New York, 1994.
• [IA1] Iserles, A., A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, Cambridge, 1996.
• [IA2] Iserles, A., Efficient Runge-Kutta methods for Hamiltonian equations, Bull. Hellenic Math. Soc. 32 (1991), 3–20.
• [KE] Kamke, E, G. Differentialgleichungen, Lösingsmethoden, und Lösingen, vol.1, Chelsea, New York, 1948.
• [KH] Karcher, H., A Gronwal l argument for error estimates of ODE integration schemes, available online at http://www.math.uni-bonn.de/people/karcher/ODEerrorViaGronwall.pdf.
• [LG] Lamb, G. L., Elements of Soliton Theory, Wiley, New York, NY, 1980.
• [LL] Landau, L. D., and Lifshitz, E. M., Mechanics, Addison-Wesley, Reading, MA, 1974.
• [LR] Lax, P. D., and Richtmyer, R. D., Survey of the stability of linear finite difference equations, Comm. Pure Appl. Math. 9 (1956), 267–293.[LE] Lorenz, E., Deterministic non-periodic flow, Journal of the Atmospheric Sciences 20 (1963), 130–141.
• [MRH] Merson, R. H., An operational method for the study of integration processes, Proc. Symposium Data Processing, Weapons Research Establishment, Salisbury, S. Australia, 1957.
• [MT] Mullins, T., The Nature of Chaos, Oxford University Press, USA, 1993.
• [PB] Palais, B., Blowup for nonlinear equations using a comparison principle in Fourier space, Commun. Pure Appl. Math 41 (1988), 165–196.
• [PDB] Polking, J., Arnold, D., and Boggess, A., Differential Equations, Second Edition, Prentice Hall, 2005.
• [KE] Pontryagin, L. S., Ordinary Differential Equations, Addison Wesley, Reading, Mass. 1962.
• [DR] Ruelle, D., Chance and Chaos, Penguin, London, 1993.
• [SJM] Sanz-Serna, J. M., Runge–Kutta schemes for Hamiltonian systems, BIT 28 (1988), 877.
• [SLF] Shampine, L. F., Numerical Solution of Ordinary Differential Equations, Chapman and Hall, New York, NY, 1994.
• [SG] Strang, G., On the Construction and Comparison of Difference Schemes, SIAM J. Numer. Anal. 5 (1968) (3), 506–517.
• [SS] Strogatz, S., Nonlinear Dynamics and Chaos, Perseus, 2000.
• [TF] Tappert, F., Numerical Solutions of the Korteweg-de Vries Equations and Its Generalizations by the Split-Step Fourier Method, in Nonlinear Wave Motion, Lectures in Applied Math., vol. 15, American Mathematical Society, Providence, RI, pp. 215–216, 1974.
• [YH] Yoshida, H., Construction of higher order symplectic integrators, Phys. Lett. A 150 (1990), 262.