# initial-value problem

## initial-value problem

[i′nish·əl ¦val·yü ‚präb·ləm]
(fluid mechanics)
A dynamical problem whose solution determines the state of a system at all times subsequent to a given time at which the state of the system is specified by given initial conditions; the initial-value problem is contrasted with the steady-state problem, in which the state of the system remains unchanged in time. Also known as transient problem.
(mathematics)
An n th-order ordinary or partial differential equation in which the solution and its first (n- 1) derivatives are required to take on specified values at a particular value of a given independent variable.
References in periodicals archive ?
In particular, we consider an initial-value problem for the nonlocal model with initial data strictly compatible with the solitary wave solution of the KdV equation or the BBM equation and then use a finite-difference scheme to solve the initial-value problem numerically.
In our ONR-funded study, we use a semianalytic Fourier-Laplace method to solve the complete initial-value problem for linear waves forced by an idealized tsunami at the lower boundary.
to approximate the solution y(x) of the initial-value problem at [x.
Equation (2) was first introduced in [12] and both global existence and blow-up results for solutions of the initial-value problem with initial data in appropriate function spaces were established.
When an initial-value problem is stiff, one will typically observe that a code based on an explicit scheme will need to use extremely small stepsizes in order to compute a stable solution as opposed to one based on an implicit scheme.
We present Fortran 90 software for the initial-value problem in ordinary differential equations, including the interfaces and how Fortran 90 language features afford the opportunity both to address different types and structures of variables and to provide additional functionality.
Until the 1990s the inverse scattering methodology was pursued almost entirely for pure initial-value problems.
Petzold, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA, 1996.
The first three chapters cover initial-value problems, and boundary-value problems solved using discrete variable methods or finite element methods, for ordinary differential equations.
12] Mahmouda and Osman, MS: On a class of spline-collocation methods for solving second-order initial-value problems.

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