# Approximate Solution of Difference Equations

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
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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

- 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