173 citations · 813 across the 30 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…
Numerical Energy Dissipation for Time-Fractional Phase-Field Equations
Chaoyu Quan, Tao Tang, Jiang Yang
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation a…
Stability analysis for the Implicit-Explicit discretization of the Cahn-Hilliard equation
Dong Li, Tao Tang
Implicit-Explicit methods have been widely used for the efficient numerical simulation of phase field problems such as the Cahn-Hilliard equation or thin film type equations. Due t…
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…
How to Define Dissipation-Preserving Energy for Time-Fractional Phase-Field Equations
Chaoyu Quan, Tao Tang, Jiang Yang
There exists a well defined energy for classical phase-field equations under which the dissipation law is satisfied, i.e., the energy is non-increasing with respect to time. Howeve…