Initial Condition


Also found in: Acronyms.

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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Our curious visitor might roam around a little more and notice a few other paradoxes in this city of ours: A remarkable number of skyscrapers and apartment blocks, but very few tenants a huge range of shopping malls, but a dearth of shoppers.Again, we revel in initial conditions, but fail in enabling our long-term success.
Additionally, the steel in initial condition was annealed at T = 450[degrees]C for t = 50 and 100 hours.
where h, k [greater than or equal to] 1 in the upper bound of the sigmas and the differential transform of initial condition is as follows:
Caption: Figure 6: Attraction basins: (a) under initial conditions (0.1, 0.1, p, [l.sub.1]) and (b) under initial condition [l.sub.1] and system parameter [xi].
Although this time exact initial conditions were applied for the sake of image reconstruction but, due to the added noise, the residues are not regenerated properly.
Devaney has one of the most popular and accepted definitions of chaos in which such systems must exhibit sensitive dependence to initial conditions, topological transitivity, and dense periodic orbits [2].
Similar to the previous section, we depict the collocation points associated with the initial conditions and boundary conditions in each case of the diffusion and wave equations for clarity of presentation.
It can be found that this new chaotic system has two isolated chaotic attractors or two disconnected chaotic attractors (named "positive attractor" and "negative attractor" in this paper), which depend on the distance between the initial points (initial conditions) and the unstable equilibrium points.
For a clear comparison, Figure 3(b) provides the highest Lyapunov exponent curves only under two initial conditions. For initial condition [[alpha].sub.1], by numerical calculation, the finite-time local Lyapunov exponents of the system at t = 15 s were [L.sub.1] = -13.01, [L.sub.2] = -13.32, [L.sub.3] = -25.42, [L.sub.4] = -26.09, [L.sub.1] < [L.sub.2] < [L.sub.3] < [L.sub.4] < 0, whereas the maximum Lyapunov exponent [L.sub.1] was below 0.
While these simulations represent some of the most accurate to date, simulations generally follow the evolution for a handful of orbits and are based upon initial conditions of quasicircular orbits obtained in the conformally flat approximation.
The sequence induced by the logistic map with this initial condition is given by:

Full browser ?