Abstract
This chapter is a summary of the elementary methods available for solving difference equations. Difference equations are used to compute quantities which may be defined recursively, such as the nth coefficient of a Taylor series or Fourier expansion or the determinant of an n × n matrix which is expanded by minors. Difference equations arise very frequently in numerical analysis where one attempts to approximate continuous systems by discrete ones.
From a drop of water a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other. So all life is a great chain, the nature of which is known whenever we are shown a single link of it.
Sherlock Holmes, A Study in Scarlet Sir Arthur Conan Doyle
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References
Chapter 2 General references on difference equations
Hildebrand, F. B., Methods of Applied Mathematics, chap. 3, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1952.
Milne-Thomson, L. M., The Calculus of Finite Differences, Macmillan and Co., London, 1953. Also see Ref. 3.
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© 1999 Springer Science+Business Media New York
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Bender, C.M., Orszag, S.A. (1999). Difference Equations. In: Advanced Mathematical Methods for Scientists and Engineers I. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3069-2_2
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DOI: https://doi.org/10.1007/978-1-4757-3069-2_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3187-0
Online ISBN: 978-1-4757-3069-2
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