The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation

By Fanhai Zeng, Changpin Li, Fawang Liu, Ian L Turner. SIAM Journal on Scientific Computing, 2013

312 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

A Simple Solver for the Fractional Laplacian in Multiple Dimensions (2018, background): “We focus in this work on the case of space-fractional diffusion and do not discuss the discretization of time-fractional differential operators, though the latter is of independent interest [30, 35, 56, 57, 59].”
An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data (2017, unknown): “1) are sufficiently smooth, for example u ∈ C2[0, T ], there are many time discretisation schemes in the literature, for example, Lubich’s fractional multistep methods [7], [30], [55], [65], [61], [62], [64], the L1 scheme and its modification [28], [26], [18], [29], [47], the spectral method [58] [”
High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II) (2015, methodology): “And for fractional derivatives, the Riemann–Liouville derivative and Caputo derivative are often adopted [2, 4, 12, 13, 16].”
A class of fractional differential hemivariational inequalities with application to contact problem (2018, background): “Recent advances in the fractional calculus concern the fractional derivative modeling in applied science, see [2,9,38], the theory of fractional differential equations, see [21], numerical approaches for the fractional differential equations, see [26,55] and the references therein.”