论文标题
用于凸域上高维的多项时空PDE的高级无网格方法
An advanced meshless approach for the high-dimensional multi-term time-space-fractional PDEs on convex domains
论文作者
论文摘要
在本文中，针对凸域上的高维度时空裂缝偏微分方程（TSFPDE）提出了高级差分（DQ）方法。首先，引入了一个高阶差异方案的家族，以离散时间折叠式衍生物，并提出了针对所考虑问题的半差异方案。我们严格证明其无条件的稳定性和错误估计。此外，我们得出了一类DQ公式来评估分数衍生物，该衍生物采用了径向基函数（RBF）作为测试函数。然后在空间离散化中使用这些DQ公式，然后提出了完全离散的DQ方案。我们的方法提供了一种灵活且高准确的替代方案，可以在凸域上解决高维的多项TSFPDE，并且与开放文献中其他可用的方法形成鲜明对比，则说明了其实际性能。数值结果证实了理论分析和我们提出的方法的能力。
In this article, an advanced differential quadrature (DQ) approach is proposed for the high-dimensional multi-term time-space-fractional partial differential equations (TSFPDEs) on convex domains. Firstly, a family of high-order difference schemes is introduced to discretize the time-fractional derivative and a semi-discrete scheme for the considered problems is presented. We strictly prove its unconditional stability and error estimate. Further, we derive a class of DQ formulas to evaluate the fractional derivatives, which employs radial basis functions (RBFs) as test functions. Using these DQ formulas in spatial discretization, a fully discrete DQ scheme is then proposed. Our approach provides a flexible and high accurate alternative to solve the high-dimensional multi-term TSFPDEs on convex domains and its actual performance is illustrated by contrast to the other methods available in the open literature. The numerical results confirm the theoretical analysis and the capability of our proposed method finally.
