Approximate Solution of Difference Equations

  • Carl M. Bender
  • Steven A. Orszag


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.


Singular Point Asymptotic Expansion Difference Equation Controlling Factor Recursion Relation 
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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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