Sentence examples for terms and nonlinear from inspiring English sources

In order to study SC generation higher order dispersion terms and nonlinear coefficient of the birefringent PCF are calculated separately for both the orthogonally polarized modes.

To achieve this purpose, a general type of the governing equation for nano-actuators, including integro-differential terms and nonlinear forces, is considered.

For complex systems (e.g. advection diffusion reaction (ADR) systems), the highest order derivative term can be nonlinear, and nonlinear nonstiff terms and nonlinear stiff terms are often mixed together.

By Balancing the order between the highest order derivative term and nonlinear term in (17), we can obtain m = 2.

By balancing the order between the highest order derivative term and nonlinear term in (38), we can obtain m 1 = m 2 = 2.

This work is concerned with positive classical solutions for a quasilinear parabolic equation with a gradient term and nonlinear boundary flux.

By balancing the order between the highest order derivative term and nonlinear term in Eq. (13), we can obtain m = 2. So, we have U = a 0 + a 1 ( D ξ α G G ) + a 2 ( D ξ α G G ) 2. (15).

First, we compare the errors and CPU time of the standard Galerkin finite element method using the backward Euler scheme and Newton iteration to treat the temporal term and nonlinear term and the Euler implicit/explicit scheme with varying time step Δt or mesh length h.

The numerical results demonstrate that the non-homogeneous boundary conditions cause the transverse vibration to deviate from the straight equilibrium, increase the natural frequencies, and lead to coexistence of square nonlinear terms and cubic nonlinear terms.

The deterministic dynamical equation for ϕ is: (5) d ϕ d t = s + r ϕ + k ϕ 2 1 − ϕ − u ϕ In many models of population dynamics in evolution and ecology, the linear growth term, rϕ, is natural, and the spontaneous term, s, and nonlinear term, kϕ 2 are not considered.

In this paper, we consider the following periodic quasilinear parabolic equation with nonlinear convection terms and weakly nonlinear sources: (1.1).