Abstract
At the heart of many problems in mathematics, physics, and engineering lies the ordinary differential equation or its numerical equivalent, the ordinary finite difference equation. Ordinary differential equations arise not only in countless direct applications, but also occur indirectly, as reductions of partial differential equations (by way of separation of variables or by transform techniques for example; cf. Chaps. 9, 11). Likewise, the probably less familiar difference equations are of inherent interest (in probability, statistics, economics, etc.) but also appear as recurrence relations in connection with differential equations or as numerical approximations to differential equations.
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References
Abramowitz, M., and Stegun, I., (editors), Handbook of Mathematical Functions, National Bureau of Standards, Applied Mathematics Series 55, Wash., D.C., 1964.
Bailey, P. B., Shampine, L. F., and Waltman, P. E., Nonlinear Two Point Boundary Value Problems, Academic Press, New York, 1968.
Birkhoff, G., and Rota, G.-C., Ordinary Differential Equations, Ginn, Boston, 1962.
Brand, L., Differential and Difference Equations, Wiley, N.Y., 1966.
Carrier, G. F., Krook, M., and Pearson, C. E., Functions of a Complex Variable-Theory and Technique, McGraw-Hill, New York, 1966.
Carrier, G. F., and Pearson, C. E., Ordinary Differential Equations, Blaisdell, Waltham, Massachusetts, 1968.
Churchill, R. V., Fourier Series and Boundary Value Problems, McGraw-Hill, New York, 1941.
Coddington, E. A., and Levinson, N., Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
Courant, R., and Hilbert, D., Methods of Mathematical Physics, vol. 1, Interscience, New York, 1953.
Forsyth, A. R., Theory of Differential Equations, Cambridge Univ. Press, New York, 1906, Dover Publications ( Reprint ), New York, 1959.
Friedman, B., Principles and Techniques of Applied Mathematics, Wiley, New York, 1956.
Friedman, B., Lectures on Applications-Oriented Mathematics, Holden-Day Inc., California, 1969.
Gantmacher, F. R., The Theory of Matrices, 2 vols., Chelsea, New York, 1959.
den Hartog, J. P., Mechanical Vibrations, McGraw-Hill, New York, 1940.
Hildebrand, F. B., Methods of Applied Mathematics, Prentice-Hall, New York, 1965.
Ince, E. L., Ordinary Differential Equations, Dover Publications, 1944.
Ince, E. L., Integration of Ordinary Differential Equations, Oliver and Boyd, Edinburgh, 1956.
Kamke, E., Differentialgleichungen Reeler Funktionen, Chelsea, London, 1947.
Kantorovich, L. V., and Krylov, V. I., Approximate Methods of Higher Analysis (C. D. Benster, trans.), Interscience, New York, 1958.
McLachlan, N. W., Ordinary Non-Linear Differential Equations in Engineering and Physical Sciences, Oxford, Second Edition, 1958.
Mikhlin, S. G., Variational Methods in Mathematical Physics, Macmillan, New York, 1964.
Mikhlin, S. G., and Smolitskiy, K. L., Approximate Methods for Solution of Differential and Integral Equations, American Elsevier, New York, 1967.
Miller, K. S., An Introduction to the Calculus of Finite Differences and Difference Equations, Henry Holt & Co., New York, 1960.
Miller, K. S., Linear Difference Equations, W. A. Benjamin, New York, 1968.
Morse, P. M., and Feshbach, H., Methods of Theoretical Physics, Parts I, II, McGraw-Hill, New York, 1953.
Murphy, G. M., Ordinary Differential Equations and Their Solutions, D. Van Nostrand, Princeton, New Jersey, 1960.
Stoker, J. J., Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience, New York, 1950.
Struble, R. A., Nonlinear Differential Equations, McGraw-Hill, New York, 1962.
Titchmarsh, E. C., Eigenfunction Expansions, Parts I, 1962, II, 1958, Oxford.
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© 1990 Van Nostrand Reinhold
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Benton, E.R. (1990). Ordinary Differential and Difference Equations. In: Pearson, C.E. (eds) Handbook of Applied Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1423-3_6
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DOI: https://doi.org/10.1007/978-1-4684-1423-3_6
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