关于具有时变系数的 Kirchhoff 型非线性动力弦方程的三层半离散格式的收敛性
偏微分方程分析
2024-04-09 v4 数值分析
数学物理
math.MP
数值分析
摘要
本文考虑具有时变系数的 Kirchhoff 型非线性动力弦方程的 Cauchy 问题。本工作的目标是开发一种时域离散化算法，能够逼近该初边值问题的解。为此，针对时间变量采用对称三层半离散格式，其中非线性项的值在中点处计算。该方法使得每个时间步的数值解可通过逆线性算子获得，从而得到二阶线性常微分方程组。建立了所提格式的局部收敛性，并且在局部时间区间上关于时间离散化步长达到二次收敛。我们使用所提算法针对多个测试问题进行了数值实验以验证其性能。可以说，所得数值结果与理论发现一致。
引用
@article{arxiv.2303.10350,
title = {On Convergence of a Three-Layer Semi-Discrete Scheme for the Nonlinear Dynamic String Equation of Kirchhoff-Type with Time-Dependent Coefficients},
author = {Jemal Rogava and Zurab Vashakidze},
journal= {arXiv preprint arXiv:2303.10350},
year = {2024}
}
备注
In the introduction section, we have included discussions on the physical relevance and applications of the problem. Additionally, we have completed a study on the stability of the three-point system obtained through the spatial discretization algorithm. The literature list has been expanded, with a focus on containing recent applications in engineering and physics