两阶段局部与非局部扩散系统的保结构数值格式
Structure-Preserving Numerical Schemes for Two-Stage Local and Nonlocal Dispersal Systems
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中文总结 AI 辅助
本文为两阶段局部-非局部扩散系统构造保结构数值格式，证明空间一致性与阈值符号保持，并在矩形区域实现与局部极限渐近相容的离散化。
中文摘要 AI 辅助
我们针对一个两阶段局部-非局部扩散系统构造并分析了保结构数值格式。在一般有界连通光滑区域上，我们证明了固定-δ空间一致性。我们引入了一个半隐式格式，该格式对每个Δt>0都唯一可解，保持非负性，并精确保留半离散谱阈值的符号。负阈值导致数值解的几何灭绝，而正阈值使数值格式的零状态线性不稳定。在矩形区域上，我们构造了一个反射笛卡尔离散化，该离散化与Neumann局部极限渐近相容，其收敛估计关于网格尺寸与相互作用尺度之比一致。数值实验说明了结构、阈值和局部极限行为。
英文摘要
We construct and analyze structure-preserving numerical schemes for a two-stage local--nonlocal dispersal system. On general bounded connected smooth habitats, we prove fixed-$δ$ spatial consistency. We introduce a semi-implicit scheme that is uniquely solvable for every $Δt>0$, preserves nonnegativity, and exactly retains the sign of the semidiscrete spectral threshold. A negative threshold yields geometric extinction of the numerical solution, while a positive threshold makes the zero state of the numerical scheme linearly unstable. On rectangular habitats, we construct a reflected Cartesian discretization that is asymptotically compatible with the Neumann local limit, with convergence estimates uniform with respect to the ratio between mesh size and interaction scale. Numerical experiments illustrate the structural, threshold, and local-limit behavior.
发表机构
- Northern Illinois University（北伊利诺伊大学）
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