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Approximate Solution of Nonlinear Differential Equations

In: Advanced Mathematical Methods for Scientists and Engineers I

Author

Listed:
  • Carl M. Bender

    (Washington University, Department of Physics)

  • Steven A. Orszag

    (Yale University, Department of Mathematics)

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.

Suggested Citation

  • Carl M. Bender & Steven A. Orszag, 1999. "Approximate Solution of Nonlinear Differential Equations," Springer Books, in: Advanced Mathematical Methods for Scientists and Engineers I, chapter 0, pages 146-204, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-3069-2_4
    DOI: 10.1007/978-1-4757-3069-2_4
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