Approximate Solution of Nonlinear Differential Equations

  • Carl M. Bender
  • Steven A. Orszag


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.


Saddle Point Nonlinear Differential Equation Local Analysis Leading Behavior Versus Versus Versus Versus Versus 
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Chapter 4 For a general discussion see Ref. 5 and

  1. 21.
    Davis, H. T., Introduction to Nonlinear Differential and Integral Equations, Dover Publications, Inc., New York, 1962.MATHGoogle Scholar

Chapter 4 For a discussion of the Thomas-Fermi equation see

  1. 22.
    Messiah, A., Quantum Mechanics, vol. II, John Wiley and Sons, Inc., New York, 1962.MATHGoogle Scholar

Chapter 4 For a discussion of phase-plane analysis see Refs. 2 and 4. For an advanced discussion see

  1. 23.
    Arnold, V. I., and Avez, A., Ergodic Problems of Classical Mechanics, W. A. Benjamin, Inc., New York, 1968.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Carl M. Bender
    • 1
  • Steven A. Orszag
    • 2
  1. 1.Department of PhysicsWashington UniversitySt. LouisUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

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