论文标题
操作员分裂，以解决动态边界条件的抽象库奇问题
Operator splitting for abstract Cauchy problems with dynamical boundary condition
论文作者
论文摘要
在这项工作中，我们研究了一类耦合的抽象库奇问题的操作员分裂方法，其中耦合是使一个问题之一为另一个问题规定了“边界类型”的额外条件。单侧耦合操作员矩阵的理论为研究此类问题的良好性提供了一个极好的框架。我们表明，使用这种机械，甚至运算符分裂方法也可以方便，有效地进行处理。我们考虑了三个特定的示例：谎言（顺序），strang和加权分裂，并在相当一般的假设下证明了这些方法的收敛以及误差边界。
In this work we study operator splitting methods for a certain class of coupled abstract Cauchy problems, where the coupling is such that one of the problems prescribes a "boundary type" extra condition for the other one. The theory of one-sided coupled operator matrices provides an excellent framework to study the well-posedness of such problems. We show that with this machinery even operator splitting methods can be treated conveniently and rather efficiently. We consider three specific examples: the Lie (sequential), the Strang and the weighted splitting, and prove the convergence of these methods along with error bounds under fairly general assumptions.
