Arbitrarily high-order accurate entropy stable essentially

nonoscillatory schemes for systems of conservation laws.

Mokhtary, "Ultra-Sharp

nonoscillatory convection schemes for high-speed steady multidimensional flow," NASA Technical Memorandum 102568, ICOMP-90-12, NASA, Washington, DC, USA, 1990.

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].

This difference can be explained by the fact that oscillatory shear measurements are limited to small strains where the matrix is still disoriented, whereas in the (

nonoscillatory) extension mode the chains can get oriented aided by the adhesion to nanofibers.

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].

For the purposes of this work, two linear PI controllers have been implemented to guarantee a fast and

nonoscillatory response of the DC motors.