Forcing function (differential equations)
From HandWiki
Short description: Function that only depends on time
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, [math]\displaystyle{ f(t) }[/math] is the forcing function in the nonhomogeneous, second-order, ordinary differential equation: [math]\displaystyle{ ay'' + by' + cy = f(t) }[/math]
References
- ↑ "How do Forcing Functions Work?". University of Washington Departments. http://depts.washington.edu/rfpk/training/tutorials/modeling/part8/10.html.
- ↑ Packard A. (Spring 2005). "ME 132" (PDF). University of California, Berkeley. p. 55. http://jagger.berkeley.edu/~pack/me132/Section7.pdf.
- ↑ Haberman, Richard (1983). Elementary Applied Partial Differential Equations. Prentice-Hall. p. 272. ISBN 0-13-252833-9. https://archive.org/details/elementaryapplie0000habe.
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