数学
积分器
操作员(生物学)
非线性系统
边界(拓扑)
数学分析
平滑的
趋同(经济学)
应用数学
联轴节(管道)
边值问题
Dirichlet边界条件
工程类
带宽(计算)
化学
经济
计算机网络
抑制因子
计算机科学
生物化学
物理
统计
基因
转录因子
经济增长
机械工程
量子力学
作者
Petra Csomós,Bálint Farkas,Balázs Kovács
出处
期刊:Ima Journal of Numerical Analysis
日期:2023-01-19
卷期号:43 (6): 3628-3655
被引量:1
标识
DOI:10.1093/imanum/drac079
摘要
Abstract We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components that describe the coupling and the dynamics in the abstract bulk- and surface-spaces, and treats the nonlinear terms similarly to an exponential integrator. The convergence proof is based on estimates for a recursive formulation of the error, using the parabolic smoothing property of analytic semigroups, and a careful comparison of the exact and approximate flows. This analysis also requires a deep understanding of the effects of the Dirichlet operator (the abstract version of the harmonic extension operator), which is essential for the stable coupling in our method. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented.
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