Search results for "Third order"
showing 6 items of 26 documents
Analytic evaluation of spectral moments
1988
In this paper an analytic procedure that drastically reduces the computational effort in evaluating the spectral moments of the response of multi-degree-of-freedom systems is presented. It is shown that the cross-spectral moments of any order of two oscillators subjected to a filtered stochastic process can be obtained in a recursive manner as a linear combination of the spectral moment of each oscillator up to the third order separately taken. A numerical procedure is also presented in order to evaluate such first few spectral moments.
Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases
2022
We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.
Global extrapolation with a parallel splitting method
1992
Extrapolation with a parallel splitting method is discussed. The parallel splitting method reduces a multidimensional problem into independent one-dimensional problems and can improve the convergence order of space variables to an order as high as the regularity of the solution permits. Therefore, in order to match the convergence order of the space variables, a high order method should also be used for the time integration. Second and third order extrapolation methods are used to improve the time convergence and it was found that the higher order extrapolation method can produce a more accurate solution than the lower order extrapolation method, but the convergence order of high order extr…
Stretched fibre based dispersion compensating module for ultra high-speed telecommunication systems
2008
International audience; In this work, the potential efficiency of a low-loss, tunable second-and third-order dispersion compensating module based on a stretched optical fibre for ultra high-speed telecommunication systems is analysed. Experimental results at a repetition rate of 640 GHz show that precise dispersion compensation could be achieved in the range of +0.038 ps/nm by means of an 11.3 cm maximum stretching of a 48 m long dispersion compensating.
Global dynamical behaviors in a physical shallow water system
2016
International audience; The theory of bifurcations of dynamical systems is used to investigate the behavior of travelling wave solutions in an entire family of shallow water wave equations. This family is obtained by a perturbative asymptotic expansion for unidirectional shallow water waves. According to the parameters of the system, this family can lead to different sets of known equations such as Camassa-Holm, Korteweg-de Vries, Degasperis and Procesi and several other dispersive equations of the third order. Looking for possible travelling wave solutions, we show that different phase orbits in some regions of parametric planes are similar to those obtained with the model of the pressure …
Properties of zeros of solutions to third order nonlinear differential equations
2013
We investigate the behavior of zeros of solutions to the certain type of third order nonlinear differential equations. We show that the behavior of zeros may be rather different and depend on the nature of nonlinearity in the equation. Main results in the paper are illustrated with a number of examples.