60 citations · 63 across the 5 of their papers we have counts for
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An energy stable and maximum bound preserving scheme with variable time steps for time fractional Allen-Cahn equation
Hong-lin Liao, Tao Tang, Tao Zhou
In this work, we propose a Crank-Nicolson-type scheme with variable steps for the time fractional Allen-Cahn equation. The proposed scheme is shown to be unconditionally stable (in…
Positive definiteness of real quadratic forms resulting from the variable-step approximation of convolution operators
Hong-lin Liao, Tao Tang, Tao Zhou
The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators.In this…
Analysis of the second order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection
Hong-lin Liao, Xuehua Song, Tao Tang +1
In this work, we are concerned with the stability and convergence analysis of the second order BDF (BDF2) scheme with variable steps for the molecular beam epitaxial model without…
ParaDiag: parallel-in-time algorithms based on the diagonalization technique
Martin J. Gander, Jun Liu, Shu-Lin Wu +2
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 stepp…
On energy stable, maximum-principle preserving, second order BDF scheme with variable steps for the Allen-Cahn equation
Hong-lin Liao, Tao Tang, Tao Zhou
In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is ener…