We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions.
Unfortunately, however, existing Filon-type asymptotic methods fail to apply to the highly oscillatory second-order differential equations when M is singular.
In this paper, we analyze and design Filon-type asymptotic methods for solving highly oscillatory second-order initial value problems q″(t)+Mq(t)="f t,q(t),q′(t)), where M is a non-singular and diagonalizable matrix having large eigenvalues and ∥M∥≫1.
In this paper, we pay attention to the error analysis for the extended Runge Kutta Nyström (ERKN) integrators proposed by Wu et al. (2010) [30] for systems of multi-frequency oscillatory second-order differential equations q″(t)+Mq(t)="f(q(t)).
In this paper we consider multi-frequency highly oscillatory second-order differential equations x″(t)+Mx t)="f t,x t),x′(t)) where high-frequency oscillations are generated by the linear part Mx t), and M is positive semi-definite (not necessarily nonsingular).
In this paper, some numerical algorithms (spectral collocation method, block spectral collocation method, boundary value method, block boundary value method, implicit Runge Kutta method, diagonally implicit Runge Kutta method and total variation diminishing Runge Kutta method) are used to solve the highly oscillatory second-order initial value problems.
Qualitative data fall into two categories: unordered qualitative data, such as ventilatory support (none, non-invasive, intermittent positive-pressure ventilation, oscillatory); and ordered qualitative data, such as severity of disease (mild, moderate, severe).
Whereas traditional WENO methods interpolate pointwise, function-based WENO methods explicitly form a non-oscillatory, high-order polynomial over the cell in question.
In the Central Pattern Generator layer some Learner-CPGs are trained which are made of coupled oscillatory neurons in order to generate basic walking trajectories.
The perturbation must arrive at the correct time in the oscillatory cycle in order to move the current position in phase space toward the unstable cycle.
