Sentence examples for based on nonstandard from inspiring English sources

In Section 3, with the triangle discretization and square discretization, we derive two discrete variational integrators for the NLS equation with variable coefficients (1) based on nonstandard finite difference methods.

For example we can consider misinterpretations I of a fully interpreted sentence S. A misinterpretation of S that makes it true is known as a nonstandard or unintended model of S. The branch of mathematics called nonstandard analysis is based on nonstandard models of mathematical statements about the real or complex number systems; see Section 4 below.

The method is applied to ten oscillators with fractional-power nonlinearities and its results are compared with those of harmonic balance techniques, Ritz procedure and numerical solutions based on nonstandard finite difference methods, in terms of displacement, velocity, energy and angular frequency, when available.

Nevertheless, patients are often are diagnosed with CLD based on nonstandard interpretations of serology or other testing that has little or no validity, or based on clinical symptoms alone [ 2, 3].

It implements exactly differentiation up to arbitrary high order based on the nonstandard analysis.

It implements conveniently differentiation up to arbitrary high order, based on the nonstandard analysis.

Now, it is meaningful to show the multi-symplectic structure of this discrete variational integrator (8) which is based on the nonstandard finite difference method.

We have derived two discrete variational integrators based on the nonstandard finite difference methods, and have presented the corresponding discrete multi-symplectic structures via multi-symplectic form formulas.

(1.6) The method used in [23, 24] is based on a nonstandard change of variables (based on some sign condition of (g'(x))) and an application of the Schauder fixed point theorem.

Thus, for the nonlinear Schödinger equation with variable coefficients (1), the multi-symplectic form formula of the scheme (8), based on the nonstandard finite difference methods, can be obtained by (11).

This c-DNS based on the recent nonstandard analysis of turbulence was carried out in a staggered grid system with a projection method on the basis of finite difference.