Oscillatory integrals are present in many applications, and their numerical approximation is the subject of this paper. Contrary to popular belief, their computation can be achieved efficiently, and in fact, the more oscillatory the integral, the more accurate the approximation. We review several existing methods, including the asymptotic expansion, Filon method, Levin collocation method and nu...

Fast evaluation of oscillatory integrals is an issue attracts much attention in many fields. In this paper, we are interested in the calculation of canonical oscillatory integrals, and the irregular oscillatory integrals are transformed into canonical ones with respect to the presences of stationary phase points or not. An improved-Levin method is proposed to calculated the canonical oscillator...

Many communicative behaviors in the animal kingdom consist of performing and recognizing specialized patterns of oscillatory motion. Here we present an approach to the representation and recognition of these oscillatory motions based on the categorical organization of a simple sinusoidal model having very specific and limited parameter values. This characterization is used to specify the types ...

We present a method to compute efficiently solutions of systems of ordinary differential equations that possess highly oscillatory forcing terms. This approach is based on asymptotic expansions in inverse powers of the oscillatory parameter, and features two fundamental advantages with respect to standard ODE solvers: firstly, the construction of the numerical solution is more efficient when th...

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...

The stability of stratified Rivlin-Ericksen fluid in porous medium in the presence of suspended particles and magnetic field has been investigated. Upon application of normal mode technique, the dispersion relation was obtained. The important results obtained in this paper include the instability of non-oscillatory modes and the stability of oscillatory modes. Also, it was found that the system...

This work extends Bilinear Discriminant Component Analysis to the case of oscillatory activity with allowed phase-variability across trials. The proposed method learns a spatial profile together with a multitaper basis which can integrate oscillatory power in a band-limited fashion. We demonstrate the method for predicting the handedness of a subject’s button press given multivariate EEG data. ...

A new diagonally implicit Runge-Kutta-Nyström (RKN) method is developed for the integration of initial-value problems for second-order ordinary differential equations possessing oscillatory solutions. Presented is a method which is three-stage fourth-order with dispersive order six and 'small' principal local truncation error terms and dissipation constant. The analysis of phase-lag, dissipatio...

Eça and Hoekstra [1] proposed a procedure for the estimation of the numerical uncertainty of CFD calculations based on the least squares root (LSR) method. We believe that the LSR method has potential value for providing an extended Richardson-extrapolation solution verification procedure for mixed monotonic and oscillatory or only oscillatory convergent solutions (based on the usual systematic...