Initial Condition

Also found in: Acronyms.

initial condition

[i′nish·əl kən′dish·ən]
(computer science)
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 It might be outdated or ideologically biased.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.
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