Work

A Magnus-based integrator for Brownian parametric semi-linear oscillators

Year: 2024

Type: article

Abstract: We introduce a numerical method for solving second-order stochastic differential equations of the form x ¨ = − ω 2 ( t ) x + f ( t , x ) + σ ( t ) ξ ( t ) , describing a class of nonlinear oscillators with non-constant frequency, perturbed by white noise ξ ( t ) . The proposed scheme takes advantages of the Magnus approach to construct an integrator for this stochastic oscillator. Its convergence properties are rigorously analyzed and selected numerical experiments on relevant stochastic oscillators are carried out, confirming the effectiveness and the competitive behavior of the proposed method, in comparison with standard integrators in the literature.

Source: Applied Mathematics and Computation

DOI: 10.1016/j.amc.2024.128610

Authors: Raffaele D'Ambrosio, Hugo de la Cruz, Carmela Scalone

Institutions: University of L'Aquila, Fundação Getulio Vargas

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,370