Xinlong Feng

TL;DR: In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes for the Allen-Cahn and Cahn-Hilliard equations were presented, and it was shown that the proposed time discretization schemes are either unconditionally energy stable, or conditionally energy stable under some reasonable stability conditions.

TL;DR: It is concluded that a real random matrix has full rank with probability 1 and a rational random matrix had full rank in the matrix computations too.

TL;DR: A high-order and energy stable scheme is developed to simulate phase-field models by combining the semi-implicit spectral deferred correction (SDC) method and the energy stable convex splitting technique, which is found very useful for producing accurate numerical solutions at small time (dynamics) as well as long time (steady state) with reasonably large time stepsizes.

TL;DR: Compared with the variational iteration method and the Adomian decomposition method, the modified homotopy perturbation technique is shown to be highly accurate, and only a few terms are required to obtain accurate computable solutions.

TL;DR: In this article, the first and second-order implicit-explicit schemes with parameters for solving the Allen-Cahn equation were investigated and theoretical justifications for the nonlinear stability of the schemes were provided, and the theoretical results were verified by numerical examples.