Difference Equations

  • Carl M. Bender
  • Steven A. Orszag


This chapter is a summary of the elementary methods available for solving difference equations. Difference equations are used to compute quantities which may be defined recursively, such as the nth coefficient of a Taylor series or Fourier expansion or the determinant of an n × n matrix which is expanded by minors. Difference equations arise very frequently in numerical analysis where one attempts to approximate continuous systems by discrete ones.


Difference Equation Independent Solution Inhomogeneous Equation Linear Difference Equation Nonlinear Difference Equation 
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Chapter 2 General references on difference equations

  1. 13.
    Hildebrand, F. B., Methods of Applied Mathematics, chap. 3, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1952.zbMATHGoogle Scholar
  2. 14.
    Milne-Thomson, L. M., The Calculus of Finite Differences, Macmillan and Co., London, 1953. Also see Ref. 3.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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