Forcing function (differential equations) explained
In a system of differential equations used to describe a time-dependent process, a forcing function is a function that appears in the equations and is only a function of time, and not of any of the other variables.[1] [2] In effect, it is a constant for each value of t.
In the more general case, any nonhomogeneous source function in any variable can be described as a forcing function, and the resulting solution can often be determined using a superposition of linear combinations of the homogeneous solutions and the forcing term.[3]
For example,
is the forcing function in the nonhomogeneous, second-order, ordinary differential equation:
Notes and References
- Web site: How do Forcing Functions Work? . University of Washington Departments . dead . https://web.archive.org/web/20030920030857/http://depts.washington.edu/rfpk/training/tutorials/modeling/part8/10.html . September 20, 2003 .
- Web site: Packard A. . ME 132 . dead . https://web.archive.org/web/20170921193859/http://jagger.berkeley.edu/~pack/me132/Section7.pdf . September 21, 2017 . PDF . Spring 2005 . . 55.
- Book: Haberman, Richard . Elementary Applied Partial Differential Equations . Prentice-Hall . 1983 . 0-13-252833-9 . 272 . registration.
