带有动态边界条件的非线性波方程的控制

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED
Rodrigo L.R. Madureira , Mauro A. Rincon , Ricardo F. Apolaya , Bruno A. Carmo
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引用次数: 0

摘要

本研究将对具有边界动态控制的非线性波方程的存在性、唯一性、能量衰减和近似数值解进行研究。将利用 Faedo-Galerkin 方法和紧凑性结果对问题进行理论分析。为了获得近似数值解,将采用有限元法和有限差分法相结合的方法,即线性化 Crank-Nicolson Galerkin 法。这种方法优化了计算,并在时间上保持了二次收敛阶次。最后,将进行数值实验,并用表格和图表说明理论收敛率,证明理论结果与数值结果的一致性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Control of a nonlinear wave equation with a dynamic boundary condition
Existence, uniqueness, energy decay, and approximate numerical solution for the nonlinear wave equation with dynamic control at the boundary is being studied in this work. The theoretical analysis of the problem will be conducted using the Faedo-Galerkin method and compactness results. To obtain the approximate numerical solution, a combined approach of the finite element method and a finite difference method will be employed, known as the linearized Crank-Nicolson Galerkin method. This method optimizes the calculations and preserves the quadratic order of convergence in time. Finally, numerical experiments are performed, and tables and graphs are presented to illustrate the theoretical convergence rates and demonstrate the consistency between theoretical and numerical results.
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来源期刊
Computers & Mathematics with Applications
Computers & Mathematics with Applications 工程技术-计算机:跨学科应用
CiteScore
5.10
自引率
10.30%
发文量
396
审稿时长
9.9 weeks
期刊介绍: Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).
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