We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components which describe the coupling and the dynamics in the bulk and on the surface, and treats the nonlinear terms by approximating the integral in the variation of constants formula. 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. Numerical experiments, including problems with dynamic boundary conditions, reporting on convergence rates are presented.

翻译：我们根据操作员的分拆得出一个数字方法,用于抽象的抛光半线性边界连接系统,该方法将描述散装和表面的组合和动态的线性部件分离出来,通过接近常数公式变异的构件处理非线性术语。聚合证据的依据是对误差的递归性配方的估计,使用分析半组的抛光性平滑属性,并仔细比较准确和大致的流量。提出了数字实验,包括动态边界条件问题,报告了趋同率。