论文标题
生物科学中一类模型的二阶非标准差异方案
Second-order nonstandard finite difference schemes for a class of models in bioscience
论文作者
论文摘要
我们考虑一个动态系统，由自主微分方程系统定义，$ω\ subset \ mathbb {r}^n $。通过使用Mickens对非线性术语的非局部近似的规则，我们构建了一个隐式的非标准有限差（NSFD）方案，该方案在存在和独特条件下是一种明确的时间可逆方案。除了基本稳定外，我们还表明，NSFD方案是二阶和域保护的，从而解决了在没有伪造解决方案的高阶非标准方案的构建方面待处理的问题，并将切线条件扩展到离散的动态系统。结果表明，新方案直接适用于基于质量动作的生物学和化学过程模型。
We consider a dynamical system, defined by a system of autonomous differential equations, on $Ω\subset\mathbb{R}^n$. By using Mickens' rule on the nonlocal approximation of nonlinear terms, we construct an implicit Nonstandard Finite Difference (NSFD) scheme that, under an existence and uniqueness condition, is an explicit time reversible scheme. Apart from being elementary stable, we show that the NSFD scheme is of second-order and domain-preserving, thereby solving a pending problem on the construction of higher-order nonstandard schemes without spurious solutions, and extending the tangent condition to discrete dynamical systems. It is shown that the new scheme applies directly for mass action-based models of biological and chemical processes.
