Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model
Numerical Analysis
2025-05-06 v1 Numerical Analysis
Abstract
We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is used for spatial discretization, while the backward Euler method and the averaged PI rule are applied for temporal discretization. The long-time stability and the finite-time error estimate of the numerical solutions are derived for both the semi-discrete-in-space scheme and the fully-discrete scheme. Furthermore, the Leray-Schauder theorem is used to derive the existence and uniqueness of the fully-discrete numerical solutions. Finally, the numerical results verify the theoretical analysis.
Keywords
Cite
@article{arxiv.2505.02517,
title = {Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model},
author = {Wenlin Qiu and Xiangcheng Zheng and Tao Guo and Xu Xiao},
journal= {arXiv preprint arXiv:2505.02517},
year = {2025}
}