一种用于生长和扩散的稳定有限差分方案

非定常对流扩散方程的无条件稳定格式

Unconditionally stable schemes for non-stationary convection-diffusion equations

针对非定常对流扩散方程，通过引入新变量和反应算子分裂的显隐式逼近，构造了无条件稳定的数值格式。

Fast stable finite difference schemes for nonlinear cross-diffusion

The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. We propose the use of two operator splitting schemes for nonlinear cross-diffusion processes in order to lower the computational load, and establish their stability properties using discrete $L^2$ energy methods. Furthermore, by attaining a stable factorization of the system matrix as a forward-backward pass, corresponding to the Thomas algorithm for self-diffusion processes, we show that the use of implicit cross-…

An energy stable and positivity-preserving scheme for the Maxwell-Stefan diffusion system

We develop a new finite difference scheme for the Maxwell-Stefan diffusion system. The scheme is conservative, energy stable and positivity-preserving. These nice properties stem from a variational structure and are proved by reformulating the finite difference scheme into an equivalent optimization problem. The solution to the scheme emerges as the minimizer of the optimization problem, and as a consequence energy stability and positivity-preserving properties are obtained.

关于具有非全局Lipschitz连续且超线性增长的漂移和扩散系数的Lévy驱动的McKean-Vlasov SDE的无限时间跨度逼近

On the infinite time horizon approximation for Lévy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion coefficients

本文研究Lévy过程驱动的McKean-Vlasov随机微分方程的数值逼近，提出了一种驯服自适应Euler-Maruyama格式，并证明了其在非全局Lipschitz连续且超线性增长系数下于有限和无限时间跨度的强收敛性。

带增长项的多孔介质方程解关于扩散指数的稳定性

Stability of solutions of the porous medium equation with growth with respect to the diffusion exponent

本文研究带增长项的多孔介质方程，通过平移初始数据正则化退化问题并优化稳定性估计，证明了解关于扩散指数的Hölder连续依赖性。