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.

翻译：在本条中,提议对锥形域的高维多时空偏差部分方程采用高级差分梯度(DQ)方法。首先,采用一系列高端差异方案,将时间偏差衍生物分解,并针对所考虑的问题提出半分解办法。我们严格证明其无条件的稳定性和误差估计。此外,我们得出了一类DQ公式,以评价利用辐射基函数(RBFs)作为测试函数的分数衍生物。在空间离散中使用这些DQ公式,然后提出完全离散的DQ方案。我们的方法提供了灵活和高准确的替代方法,用以解决在锥形域的高维多维的TSFPDDs及其实际性能,与公开文献中的其他方法相对照。数字结果证实了理论分析以及我们拟议方法最终的能力。