A functional differential equation is a differential equation with deviating argument. That is, a functional differential equation is an equation that contains a function and some of its derivatives evaluated at different argument values.[1]
Functional differential equations find use in mathematical models that assume a specified behavior or phenomenon depends on the present as well as the past state of a system.[2] In other words, past events explicitly influence future results. For this reason, functional differential equations are more applicable than ordinary differential equations (ODE), in which future behavior only implicitly depends on the past.
^Kolmanovskii, V.; Myshkis, A. (1992). Applied Theory of Functional Differential Equations. The Netherlands: Kluwer Academic Publishers. ISBN 0-7923-2013-1.
^Hale, Jack K. (1971). Functional Differential Equations. United States: Springer-Verlag. ISBN 0-387-90023-3.
and 21 Related for: Functional differential equation information
In mathematics, a differentialequation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...
such an equation differs from integral and differentialequations through a similar change of variable. A functionaldifferentialequation of delay differential...
hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e...
dynamical system and differentialequation topics, by Wikipedia page. See also list of partial differentialequation topics, list of equations. Deterministic...
coupling constant. Mathematically, FRG is based on an exact functionaldifferentialequation for a scale-dependent effective action. In quantum field theory...
for ordinary differentialequations are methods used to find numerical approximations to the solutions of ordinary differentialequations (ODEs). Their...
n, this relation is called the translation functionalequation, cf. Schröder's equation and Abel equation. On a logarithmic scale, this reduces to the...
for partial differentialequations is the branch of numerical analysis that studies the numerical solution of partial differentialequations (PDEs). In...
Stochastic partial differentialequations (SPDEs) generalize partial differentialequations via random force terms and coefficients, in the same way ordinary...
mathematics. Fractional differentialequations, also known as extraordinary differentialequations, are a generalization of differentialequations through the application...
integral equations may be viewed as the analog to differentialequations where instead of the equation involving derivatives, the equation contains integrals...
f(1-x)=1-f(x)} for 0≤x≤1,{\displaystyle 0\leq x\leq 1,} and the functionaldifferentialequation f′(x)=2f(2x){\displaystyle f'(x)=2f(2x)} for 0≤x≤1/2.{\displaystyle...
find the maxima and minima of a function. Equations involving derivatives are called differentialequations and are fundamental in describing natural...
and Partial DifferentialEquations". 1964. "A Course of Higher Mathematics Vol 5 Integration and Functional Analysis". 1964. "Differential and Integral...
In mathematics, an abstract differentialequation is a differentialequation in which the unknown function and its derivatives take values in some generic...
the functionaldifferential (or variation or first variation) is defined. Then the functional derivative is defined in terms of the functional differential...
Global Information