  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.
