# boundary value problem

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## boundary value problem

[′bau̇n·drē ‚val·yü ‚präb·ləm]
(mathematics)
A problem, such as the Dirichlet or Neumann problem, which involves finding the solution of a differential equation or system of differential equations which meets certain specified requirements, usually connected with physical conditions, for certain values of the independent variable.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
These boundary values are fed into the NEW android app.
Let u, v be two solutions of (1) with the partial homogeneous boundary values (4) and with the initial values [u.sub.0], [v.sub.0], respectively.
In Section 3, we establish analogues of results from Section 2, in terms of smoothness with respect to boundary values, for solutions of the nonlocal problem (1.1), (1.2).
The numerical results obtained were everywhere finite, free of singularities, and confirmed the well-known prediction that [u.sub.RS.sup.(p)] and [u.sub.RS.sup.(s)] reproduce the boundary values assumed in their derivation ([partial derivative][u.sub.RS.sup.(p)]/[partial derivative]z [right arrow] ik and [u.sub.RS.sup.(s)] [right arrow] 1 as z [right arrow] 0) but not the compatible values ([u.sub.RS.sup.(p)] [right arrow] 1 and [u.sub.RS.sup.(s)]/[partial derivative]z [right arrow] ik) which are implied in the classical postulate that the aperture field is the same as the unperturbed geometrical field incident on the screen.
Data from our previous work was included in the more recent paper because we needed "boundary values" between or below which we were looking for a threshold or a critical level.
Liu, "Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations," International Journal of Differential Equations, vol.
These boundary values are step functions that violate the wave equation and are the probable cause of the fact, shown in Appendix B, that the Rayleigh-Sommerfeld integrals also do not obey the wave equation in the immediate proximity of the aperture plane.
On the other hand, because of the wide mathematical and physical background, the existence of positive solutions for nonlinear integer-order boundary values problems with p-Laplacian operator has received wide attention (see [8, 12, 13, 21, 24-29]).

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