On the numerical solution of stochastic oscillators driven by time-varying and random forces

TL;DR

This paper introduces a specialized trigonometric stochastic numerical method for solving high-frequency linear oscillators influenced by nonlinear time-varying and random forces, supported by theoretical analysis and numerical experiments.

Contribution

It presents a novel numerical approach tailored for high-frequency stochastic oscillators with time-varying forces, combining theoretical insights and practical validation.

Findings

Effective numerical method for high-frequency stochastic oscillators

Theoretical analysis confirms stability and accuracy

Numerical experiments demonstrate practical applicability

Abstract

In this work, we provide a specifc trigonometric stochastic numerical method for linear oscillators with high constant frequencies, driven by a nonlinear time-varying force and a random force. We present some theoretical considerations and numerical experiments on popular related physical models.