Sentence examples for solution of the limiting from inspiring English sources

Let be any solution of the limiting equation (2.12), passing through, such that for all.

holds, where is a positive characteristic solution of the limiting equation (2.4) corresponding to the set of characteristic values (2.8).

where is any solution of the limiting equation (2.12) of (2.7), which passes through such that for all.

We prove that as the lattice parameter goes to zero, for a finite time interval, a modified discrete model converges to the strong solution of the limiting PDE with first-order convergence rate.

Also, we assume that the compact set in satisfies for all and for all, where is any solution of the limiting equation of (2.12) and (2.7).

where Up,μ(x)=Up,μ(|x|) is the unique radial solution of the limiting problem with U p, μ ( 1 ) = ( N − t ) N − p 1 p ∗ ( t ) − p. Open image in new window.

The validity was also proved by a comparison with an analytical solution for the limiting case of predominating dispersion.

We give an asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation.

The error equation between the solutions of the limiting equation and that of the current one is considered as a perturbation equation in the fixed- point and stability analyses.

The comparison between the solutions of the limiting differential equation and those of the perturbed one based on Perron-type results has been studied classically for ordinary differential equations and more recently for the case of functional equations [10, 21, 22].

The solutions coincide with the known classical solutions for the limiting cases of constitution, geometry and loading.