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. 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. For example, f ( t ) {\displaystyle f(t)} is the forcing function in the nonhomogeneous, second-order, ordinary differential equation: a y ″ + b y ′ + c y = f ( t ) {\displaystyle ay''+by'+cy=f(t)}

Function that only depends on time

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

References

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

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