Ziemer, Rodger E. Department of Electrical and Computer Engineering, University of Colorado, Colorado Springs, Colorado.
- Linear constant-coefficient equations
- Nonhomogeneous linear equations
- Nonlinear difference equations
- Approximating continuous-time systems
- Partial difference equations
- Additional Reading
A relationship between one or more independent variables, one or more dependent variables, and differences of those variables. Difference equations arise in the analysis of discrete systems (for example, a string loaded along its length with small masses), in the solution of differential equations by means of digital computers, in the implementation of digital filters, and in the discrete-time control of systems. An ordinary difference equation expresses a relationship between an independent variable and one or more dependent variables, , and so forth, and any successive differences of . The first forward difference of , relative to the increment , is defined by Eq. (1).
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