A double-parameter shifted convolution quadrature formula and its application to fractional mobile/immobile transport equations

In this article, we propose a novel second-order shifted convolution quadrature (SCQ) formula including both a shifted parameter $\theta$ and a new variable parameter $\delta$. We prove the second-order truncation error of the novel formula for the time-fractional derivative, and derive the nonnegative property of the formula’s weights. Combining the novel formula with the finite element method, we develop a high order numerical scheme for fractional mobile/immobile transport equations. Furthermore, we analyze the stability and error estimate of the numerical method. We present numerical tests to further validate our theoretical results.