# Initial Condition

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## initial condition

[i′nish·əl kən′dish·ən]
(computer science)
(meteorology)
A prescription of the state of a dynamical system at some specified time; for all subsequent times the equations of motion and boundary conditions determine the state of the system; the appropriate synoptic weather charts, for example, constitute a (discrete) set of initial conditions for a forecast; in many contexts, initial conditions are considered as boundary conditions in the dimension of time.

## Initial Condition

in the mathematical analysis of a process the state of the process at a given moment of time, taken as the initial moment. If the process is described by a differential equation, then the problem of finding solutions for a given initial condition is called the Cauchy problem. An initial condition for the equation

consists in specifying y, dy/dt, . . . , (dn-1y)/dtn-1 for a value t = t0. If n = 2 and y = y(t) is the law of motion of a point mass, then the initial condition specifies the position and velocity of the point at the moment t = t0 An initial condition for a partial differential equation is similarly defined. Thus, for the equation

of a free vibrating string, where u(t, x) is the deviation of the point x of the string at the moment t from the position of equilibrium on the x-axis, the initial condition specifies the initial shape uǀt = t0 = f(x) of the string and the initial velocities δu/ δ/1,= t0 of the points of the string. Any other argument may play the role of time. An initial condition is then specified for some value of that argument.

References in periodicals archive ?
In these calculations, Equation 6 was numerically solved as an initial value problem with L(a, t)|[sub.
is a continuous mapping such that r [right arrow] g(t, r) is nondecreasing and the initial value problem
ED),Applications of nonstandard methods for initial value problems, World Scientific, Singapore.
YAJIMA, Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media, Supp.
An integro-differential inequality is proposed together with an application to initial value problems.
In practice, SODEs are frequently treated as either initial value problems (IVPs) or boundary value problems (BVPs).
It must be stated here that the method can handle effectively higher order initial value problems.
15) to develop a discrete analogue of the initial value problem.
Applying shooting method, we reduce it into initial value problem.
Kaleva showed in [18; 19] that if continuous and satisfies the Lipschitz condition with respect to u , then there exists a unique local solution for the fuzzy initial value problem u'(t) = f (t,u), u(0) = [u.
In this research, we have initiated a new technique for solving fuzzy initial value problem.
There are two methods for obtaining precise approximations to the solution of a nonlinear initial value problem, numerical methods and analytical methods.

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