Related papers: Higher order phase averaging for highly oscillator…
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide…
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…
Phase reduction is a powerful technique in the study of nonlinear oscillatory systems. Under certain assumptions, it allows us to describe each multidimensional oscillator by a single phase variable, giving rise to simple phase models such…
This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived…
A pure frequency domain method for the computation of periodic solutions of nonlinear ordinary differential equations (ODEs) is proposed in this study. The method is particularly suitable for the analysis of systems that feature distinct…
We propose a new class of high-order time-marching schemes with dissipation user-control and unconditional stability for parabolic equations. High-order time integrators can deliver the optimal performance of highly-accurate and robust…
Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction…
We show that, for appropriate combinations of the values of the delay and the forcing frequency, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant…
We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly-oscillatory. Thanks to an averaging…
In this paper, we propose, analyze, and test a new fully discrete, efficient, decoupled, stable, and practically second-order time-stepping algorithm for computing MHD ensemble flow averages under uncertainties in the initial conditions and…
A single-step high-order implicit time integration scheme with controllable numerical dissipation at high frequencies is presented for the transient analysis of structural dynamic problems. The amount of numerical dissipation is controlled…
In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…
Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…
In this paper, we develop a novel phase retrieval approach to reconstruct x-ray differential phase shift induced by an object. A primary advantage of our approach is a higher-order accuracy over that with the conventional linear…
A low out-degree orientation directs each edge of an undirected graph with the goal of minimizing the maximum out-degree of a vertex. In the parallel batch-dynamic setting, one can insert or delete batches of edges, and the goal is to…
A model of phase transitions with coupling between the order parameter and its gradient is proposed. It is shown, that this nonlinear model is suitable for the description of phase transitions accompanied by the formation of spatially…
In this paper, we extend the method proposed by Cochelin and Vergez [A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, 324 (2009) 243-262] to the case of…
This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
A new model for time series with a specific oscillation pattern is proposed. The model consists of a hidden phase process controlling the speed of polling and a nonparametric curve characterizing the pattern, leading together to a…