在大于其空间图案的尺度上整体离散化Swift-Hohenberg方程
Holistically discretise the Swift-Hohenberg equation on a scale larger than its spatial pattern
AI总结：
提出一种在大于空间图案尺度上整体离散化Swift-Hohenberg方程的新方法，直接生成图案振幅演化的离散格式，具有中心流形理论支持并纳入物理边界，为图案选择计算探索提供有力工具。
摘要：
我引入了一种创新方法，用于推导表现出空间图案演化的偏微分方程系统的数值模型。新方法直接产生图案振幅演化的离散化，在有限网格尺寸$h$下具有中心流形理论的严格支持，并自然地纳入物理边界。本文针对Swift-Hohenberg方程给出的结果表明，该方法将成为计算探索一般图案选择的有力工具。借助计算机代数，这些技术可应用于各种方程，以推导出准确且稳定捕获动力学（包括可能受迫边界的影响）的数值模型。
英文摘要：
I introduce an innovative methodology for deriving numerical models of systems of partial differential equations which exhibit the evolution of spatial patterns. The new approach directly produces a discretisation for the evolution of the pattern amplitude, has the rigorous support of centre manifold theory at finite grid size $h$, and naturally incorporates physical boundaries. The results presented here for the Swift-Hohenberg equation suggest the approach will form a powerful method in computationally exploring pattern selection in general. With the aid of computer algebra, the techniques may be applied to a wide variety of equations to derive numerical models that accurately and stably capture the dynamics including the influence of possibly forced boundaries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
