In this work, we propose a trigonometric stochastic numerical method for linear oscillators with high constant frequencies, driven by a nonlinear time-varying force and a random force. The scheme is obtained by applying the variation-of-constants formula and Filon quadrature, that is notoriously more effective for oscillating integrands. The development of the scheme and its analysis is equipped by numerical experiments on popular related physical models, confirming the effectiveness of the approach.

中文翻译：

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由时变力驱动的随机振荡器的 Filon 正交

在这项工作中，我们提出了一种由非线性时变力和随机力驱动的具有高恒定频率的线性振荡器的三角随机数值方法。该方案是通过应用常数变化公式和 Filon 求积获得的，众所周知，这对于振荡被积函数更有效。该方案的开发及其分析配备了流行的相关物理模型的数值实验，证实了该方法的有效性。