nonoscillatory

Arbitrarily high-order accurate entropy stable essentially nonoscillatory schemes for systems of conservation laws.

The inviscid fluxes are calculated using the fifth-order weighted essentially nonoscillatory (WENO) scheme, while the central differencing technique is applied to the viscous fluxes.

A solution {[y.sub.n]} of (1) is said to be oscillatory if, for every positive integer [n.sub.0] > 0, there exists n [greater than or equal to] [n.sub.0] such that [y.sub.n][y.sub.n+1] [less than or equal to] 0; otherwise {[y.sub.n]} is said to be nonoscillatory. In the sequel, unless otherwise specified, when we write a functional inequality, it will be assumed to hold for all n sufficiently large.

As usual a solution of (1) is said to be oscillatory if it is neither eventually positive nor eventually negative; else it is nonoscillatory.

Section 2 discussed the oscillatory and nonoscillatory properties of the third-order linear differential equation.

In this paper, an optimized fifth-order symmetric WENO (weighted essentially nonoscillatory) method (WENO-SYM3) based on the three templates is proposed [8-11].

Alsaedi, "Existence of nonoscillatory solutions for fractional neutral differential equations," Applied Mathematics Letters, vol.

Yan, "Existence of nonoscillatory solutions of higher-order neutral differential equations with distributed deviating arguments," Acta Mathematicae Applicatae Sinica, vol.

In particular, (1) with [lambda]c(t) instead of c(t) is said to be conditionally oscillatory if there exists a constant [[lambda].sub.0] such that this equation is oscillatory for [lambda] > [[lambda].sub.0] and nonoscillatory for [lambda] < [[lambda].sub.0].