Approximate Solution of Nonlinear Differential Equations
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.
KeywordsSaddle Point Nonlinear Differential Equation Local Analysis Leading Behavior Versus Versus Versus Versus Versus
Unable to display preview. Download preview PDF.
Chapter 4 For a general discussion see Ref. 5 and
Chapter 4 For a discussion of the Thomas-Fermi equation see
Chapter 4 For a discussion of phase-plane analysis see Refs. 2 and 4. For an advanced discussion see
- 23.Arnold, V. I., and Avez, A., Ergodic Problems of Classical Mechanics, W. A. Benjamin, Inc., New York, 1968.Google Scholar