Analysis of the Chang–Cooper discretization scheme for a class of Fokker–Planck equations
Analysis of the Chang–Cooper discretization scheme for a class of Fokker–Planck equations
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一类 Fokker-Planck 方程的 Chang-Cooper 离散化格式分析
DOI：
10.1515/jnma-2015-0018
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发表时间：
2015
影响因子：
3
通讯作者：
A. Borzì
中科院分区：
文献类型：
--
作者：
M. Mohammadi;A. Borzì
摘要 研究一类Fokker-Planck方程的Chang-Cooper离散化格式。这些抛物型方程控制着随机过程的概率密度函数的时间演化，从而保证了密度函数的正性和总概率的保守性。结果表明，Chang-Cooper 格式结合向后一阶和二阶时间有限差分可提供稳定且精确的保守且正解。这些特性在理论上得到了数值实验的证明和验证。
Abstract The Chang-Cooper discretization scheme for a class of Fokker-Planck equations is investigated. These equations of parabolic type govern the time evolution of the probability density function of stochastic processes, such that positivity of the density function and conservativeness of the total probability is guaranteed. It is shown that the Chang-Cooper scheme combined with backward first- and second-order finite differencing in time provides stable and accurate solutions that are conservative and positive. These properties are theoretically proven and validated by numerical experiments.