Forcing function (differential equations)

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

References

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

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[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.

[haberman-3] Haberman, Richard (1983). Elementary Applied Partial Differential Equations. Prentice-Hall. p. 272. ISBN 0-13-252833-9.

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