Structure-Preserving Numerical Schemes for Two-Stage Local and Nonlocal Dispersal Systems

Abstract

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.

Structure-Preserving Numerical Schemes for a Time-Fractional Porous Medium Equation with Nonlocal Pressure
Łukasz Płociniczak, Hubert Woszczek
arXiv24 Oct 2026PreprintCC BY 4.0Full textAnalysis & PDEs Numerical analysis & scientific computingarXiv
Uniqueness and structure-preserving numerical simulations for an Ultrahyperbolic Schrödinger equation
Özlem Kaytmaz, Muhammed Hasdemir
Scientific Reports7 Oct 2026Peer-reviewedCC BY-NC-ND 4.0Full textMathematical physicsCrossref
Structure-preserving upwind Lagrange multiplier schemes for solid-state dewetting with a logarithmic Flory--Huggins potential
Qiong-Ao Huang, Ying-wei Wang, Cheng Yuan
arXiv29 Sep 2026PreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingarXiv
Asymptotically Compatible Variational Energy Dissipation Laws and Structure-Preserving Variable-Step Linear Relaxation Schemes for a Subdiffusive Tumor-Nutrient Model
Hui Yu, Zhaoyang Wang, Ping Lin
arXiv29 Oct 2026PreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
On structure-preserving and pointwise conservative continuous DG schemes for hyperbolic systems
Rémi Abgrall, Michael Dumbser, Pierre-Henri Maire +1
arXiv6 Oct 2026PreprintCC BY-NC-SA 4.0Full textNumerical analysis & scientific computingarXiv

Cite

BibTeX RIS

BibTeX

@misc{uba2026structurepreserving,
  title = {{Structure-Preserving Numerical Schemes for Two-Stage Local and Nonlocal Dispersal Systems}},
  author = {Markjoe O. Uba},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29524},
  eprint = {2609.29524},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29524},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Structure-Preserving Numerical Schemes for Two-Stage Local and Nonlocal Dispersal Systems
AU  - Markjoe O. Uba
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.29524
UR  - https://arxiv.org/abs/2609.29524
AB  - 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.
ER  -

Abstract

Related

Cite