Abstract
One cannot hope to obtain exact solutions to most nonlinear differential equations. As we saw in Chap. 1, there are only a limited number of systematic procedures for solving them, and these apply to a very restricted class of equations. Moreover, even when a closed-form solution is known, it may be so complicated that its qualitative properties are obscured. Thus, for most nonlinear equations it is necessary to have reliable techniques to determine the approximate behavior of the solutions.
It is quite a three pipe problem, and I beg that you won’t speak to me for fifty minutes.
—Sherlock Holmes, The Red-Headed League Sir Arthur Conan Doyle
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References
Chapter 4 For a general discussion see Ref. 5 and
Davis, H. T., Introduction to Nonlinear Differential and Integral Equations, Dover Publications, Inc., New York, 1962.
Chapter 4 For a discussion of the Thomas-Fermi equation see
Messiah, A., Quantum Mechanics, vol. II, John Wiley and Sons, Inc., New York, 1962.
Chapter 4 For a discussion of phase-plane analysis see Refs. 2 and 4. For an advanced discussion see
Arnold, V. I., and Avez, A., Ergodic Problems of Classical Mechanics, W. A. Benjamin, Inc., New York, 1968.
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© 1999 Springer Science+Business Media New York
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Bender, C.M., Orszag, S.A. (1999). Approximate Solution of Nonlinear Differential Equations. In: Advanced Mathematical Methods for Scientists and Engineers I. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3069-2_4
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DOI: https://doi.org/10.1007/978-1-4757-3069-2_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3187-0
Online ISBN: 978-1-4757-3069-2
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