Initial Condition

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 ?
variables characterising initial conditions, such as the degree of
The second alternative initial condition was constructed from the population dynamics of a typical fish population.
Consider this initial condition along with the requirements for applying the existence-uniqueness theorem.
The latter "improper" initial condition for Regime B led to a higher diffusivity at the inner wall due to a moderate influence initially from the Regime A mechanism.
For certain boundary and initial conditions analytical solutions to equation (4) can be obtained.
For any initial condition [delta]x, the quadratic term -[delta][x.
The divergence in the pathway demonstrated initial condition sensitivity.
In order to know that the encrypted image can resist the exhaustive attacks it should be proven that it has a large key space and high sensitivity to initial conditions.
for "The Initial Condition," work by Damon Harris, at The Wave Gallery, 547 Blair Ave.
Thus the solution naturally splits into two terms the first one corresponds to the response of the initial condition and the second one is entirely due to the external input function h(t).
IAG said last month it had ruled out raising its bid for Vueling, although it could waive the initial condition it set of a minimum acceptance of 90 percent of non-IAG shareholders.

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