Forcing function (differential equations)

This article is about a mathematical concept. For other uses, see Forcing function.

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, ${\displaystyle f(t)}$ is the forcing function in the nonhomogeneous, second-order, ordinary differential equation: $${\displaystyle ay''+by'+cy=f(t)}$$

References

1. "How do Forcing Functions Work?". University of Washington Departments. Archived from the original on September 20, 2003.
2. Packard A. (Spring 2005). "ME 132" (PDF). University of California, Berkeley. p. 55. Archived from the original (PDF) on September 21, 2017.
3. Haberman, Richard (1983). Elementary Applied Partial Differential Equations. Prentice-Hall. p. 272. ISBN 0-13-252833-9.