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Approximate Solution of Difference Equations

  • Carl M. Bender
  • Steven A. Orszag
Chapter

Abstract

Difference equations (recursion relations) occur so frequently in applied mathematics that we allot a full chapter to a discussion of the behavior of their solutions. We will study the problem of determining the behavior of a n , the solution to a difference equation, as n → ∞. This is the most common kind of asymptotics problem involving difference equations.

Keywords

Singular Point Asymptotic Expansion Difference Equation Controlling Factor Recursion Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

Chapter 5 For a general discussion of asymptotic methods see Ref. 14. The Stirling series is discussed in Ref. 12. For a discussion of nonlinear recursion relations see Ref. 16 and

  1. 24.
    Stein, P. R., and Ulam, S., “Lectures on Nonlinear Algebraic Transformations,” in A. O. Barut (Ed.), Studies in Mathematical Physics, Reidel, Dordrecht, Holland, 1970.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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