Sentence examples for equation whenever from inspiring English sources

We study the oscillatory behavior that arises in solutions of a dispersive numerical scheme for the Hopf equation whenever the classical solution of that equation develops a singularity.

It should be noted that we have the classical advective flow equation when (alpha=1) and standard diffusion equation whenever (alpha=2).

Indeed, it is well-known that one can always find the desired feedback control through the corresponding Riccati equation whenever a deterministic LQ is solvable.

Najati and Zamani Eskandani [15] have established the general solution and the generalized Hyers-Ulam stability for a mixed type of cubic and additive functional equation, whenever is a mapping between two quasi-Banach spaces (see also [16, 17]).

We say that u is an approximate solution for fractional integro-differential equation whenever we could obtain a sequence of functions ({u_{n}} _{ngeq1}) with (u_{n}to u).

In the present paper we investigate the general solution of the functional equation (1.6) when is a mapping between vector spaces, and we establish the generalized Hyers-Ulam stability of this functional equation whenever is a mapping between two quasi-Banach spaces.

Computations are made with this model to situations typical of forward Raman scattering and beatwave; results are in accordance with other computational methods such as full electromagnetic Vlasov-Maxwell code or envelope equations whenever they can be used.

We use here the standard notation in functional equations: whenever it makes sense, x t ∈ M ˜ denotes the function θ ↦ x ( t + θ ).

Make note of when things didn't work and illustrate with equations whenever possible.

In fact, this partial differential equation holds whenever C is twice differentiable with respect to s and once with respect to τ; see[2].

Moreover, it satisfies, as a function of t, the two-point boundary value conditions (2) and solves equation (1) whenever (t neq s).