The purpose of this book is to present a self-contained and up-to-date survey of numerical
treatment for the so-called time-fractional diffusion model and their mathematical analysis …

In 2008, Maday and Ronquist introduced an interesting new approach for the direct parallel-
in-time (PinT) solution of time-dependent PDEs. The idea is to diagonalize the time stepping …

Solving evolutionary equations in a parallel-in-time manner is an attractive topic. The
iterative algorithm based on the block α-circulant preconditioning technique has shown …

Solving the linear system is often the major computational burden when a forward-backward
evolutionary equation must be solved in a problem, where is the so-called all-at-once matrix …

We investigate an inverse problem with quasi-boundary value regularization for
reconstructing a source term of time-space fractional diffusion equations from the final …

We investigate a second-order accurate time-stepping scheme for solving a time-fractional
diffusion equation with a Caputo derivative of order\(\alpha\in (0, 1)\). The basic idea of our …

In this work we investigate an inverse problem of recovering a time-dependent potential in a
semilinear subdiffusion model from an integral measurement of the solution over the …

In this paper we propose a model reduction technique to speed up the diagonalization-
based parallel-in-time (ParaDIAG) preconditioner, for iteratively solving all-at-once systems …

For solving the semilinear fractional differential equations with the nonsmooth force term, we
construct a class of Runge–Kutta-based convolution quadrature. Moreover, we analyse the …

Solving multiscale diffusion problems is often computationally expensive due to the spatial
and temporal discretization challenges arising from high-contrast coefficients. To address …