Xiujun Cheng

TL;DR: The highlight is that the time discretization is achieved by applying a second-order, one-step and linearized method, which is sharp contrast to the extrapolated Crank–Nicolson method or the usual second- order linearized schemes.

TL;DR: A novel two-level linearized compact alternating direction implicit (ADI) scheme is proposed for solving two-dimensional nonlinear reaction–diffusion equations and the existence and uniqueness of the numerical solutions are proved.

TL;DR: In this article, the authors studied the most probable transition pathways and maximal likely trajectories in a genetic regulation model of the transcription factor activator's concentration evolution, with Gaussian noise and non-Gaussian stable Levy noise in the synthesis reaction rate taking into account, respectively.

TL;DR: This work has conducted a series of numerical experiments in "regulating" the likelihood of gene transcription by tuning asymmetric stable Lévy noise indexes, and offers insights for possible ways of achieving gene regulation in experimental research.

TL;DR: In this article, the analysis of the linear method and compact method for solving delay reaction-diffusion equation is concerned. But the analysis is restricted to the case where the two methods are asymptotically stable.