Approximate Solution of Nonlinear Differential Equations

Carl M. Bender and Steven A. Orszag
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Carl M. Bender: Washington University, Department of Physics
Steven A. Orszag: Yale University, Department of Mathematics

Chapter Chapter Four in Advanced Mathematical Methods for Scientists and Engineers I, 1999, pp 146-204 from Springer

Abstract: 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.

Keywords: Saddle Point; Nonlinear Differential Equation; Local Analysis; Leading Behavior; Versus Versus Versus Versus Versus (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-1-4757-3069-2_4

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