论文标题
部分可观测时空混沌系统的无模型预测
The Neumann boundary condition for the two-dimensional Lax-Wendroff scheme
论文作者
论文摘要
我们使用稳定器研究了二维宽松的宽温德罗夫方案的稳定性，该方案近似于传输方程的溶液。首先在整个空间中分析该问题，以证明所谓的能量方法为此有限差异方案产生了最佳稳定性标准。然后，当运输运营商即将上升时，我们处理半个空间的情况。在数值级别，我们强制执行Neumann外推边界条件，并表明相应的方案是稳定的。最终，我们分析了交通运输官相对于双方的季度。然后，我们在边界的每一侧强制执行Neumann外推边界条件，并在数值角处提出外推边界条件，以维持整个数值方案的稳定性。
We study the stability of the two-dimensional Lax-Wendroff scheme with a stabilizer that approximates solutions to the transport equation. The problem is first analyzed in the whole space in order to show that the so-called energy method yields an optimal stability criterion for this finite difference scheme. We then deal with the case of a half-space when the transport operator is outgoing. At the numerical level, we enforce the Neumann extrapolation boundary condition and show that the corresponding scheme is stable. Eventually we analyze the case of a quarter-space when the transport operator is outgoing with respect to both sides. We then enforce the Neumann extrapolation boundary condition on each side of the boundary and propose an extrapolation boundary condition at the numerical corner in order to maintain stability for the whole numerical scheme.
