论文标题
伪偏射式陌生分裂方法，用于透明边界条件的线性分散问题
A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions
论文作者
论文摘要
目前的工作提出了一个线性分散方程的二阶时间拆分方案，其对流系数受透明边界条件的约束。为了实现空间离散化，考虑了双重凝固性 - galerkin方法，该方法具有光谱的准确性。在这种情况下构建二阶分裂方案的主要困难在于在子问题的边界处的兼容条件。特别是，在对流部分中存在流入边界条件是为了减少的。为了克服此问题，引入了保留二阶准确性的修改后的Strang分裂方案。对于此数值方案，进行了稳定性分析。另外，数值结果被证明可以支持理论推导。
The present work proposes a second-order time splitting scheme for a linear dispersive equation with a variable advection coefficient subject to transparent boundary conditions. For its spatial discretization, a dual Petrov--Galerkin method is considered which gives spectral accuracy. The main difficulty in constructing a second-order splitting scheme in such a situation lies in the compatibility condition at the boundaries of the sub-problems. In particular, the presence of an inflow boundary condition in the advection part results in order reduction. To overcome this issue a modified Strang splitting scheme is introduced that retains second-order accuracy. For this numerical scheme a stability analysis is conducted. In addition, numerical results are shown to support the theoretical derivations.
