Sentence examples for reduced difference equation from inspiring English sources

Since there is no restriction on the distance between the consecutive switching moments of the argument, the reduced difference equation for (5) is of the nonautonomous type given by u k+1)=fbigl k,u k bigr), quad kinmathbb{N}, (10) where (f k,u k))=u k){mathrm{e}}^{(a-bu k))g(k)}).

Naturally, analytical models that can be reduced to difference equations can also be represented with their formalism.

Furthermore, a Darboux transformation of a reduced differential-difference equation system of the latter discrete hierarchy is obtained.

By the change of variables, (1.1) reduces to the difference equation (1.11).

It reduces to the difference equation (1) that represents the dynamic of CO2 accumulation, if we take the budget constraint of the government.

Next, note that if α i + β i + γ i = 0 for i = 1 or 2, then at least one of the members of system (1) becomes trivial causing the latter to reduce to a difference equation.

Substituting equation (36) into equation (3), we have the first symmetry reduced equation of equation (3) varphi_{xixixieta}+4varphi_{xixi}+4varphi_{xieta}+4varphi _{xi}varphi_{xieta}+2varphi_{xixi} varphi_{eta}+3varphi_{yy}=0.

We see that a differential equation with piecewise constant argument, whose distance between the two consecutive switching moments is equal, can be reduced into an autonomous difference equation.

To the best of our knowledge, it is the first time in the literature that a differential equation with piecewise constant argument of generalized type is reduced into a nonautonomous difference equation.

Let us reduce (5) into a difference equation.

Thus, (3.7) reduces to the delay difference equation (4.10).