Long-time behavior of multi-step Finite Difference schemes with boundary via steepest descent and analytic combinatorics
Numerical Analysis
2026-03-24 v1 Numerical Analysis
Abstract
We demonstrate how steepest descent arguments and singularity analysis from analytic combinatorics allow for an accurate description of the behavior of linear numerical schemes -- including the notorious leap-frog scheme -- in presence of stable and unstable boundary conditions in the long-time limit.
Keywords
Cite
@article{arxiv.2603.21899,
title = {Long-time behavior of multi-step Finite Difference schemes with boundary via steepest descent and analytic combinatorics},
author = {Thomas Bellotti and Tommaso Tenna},
journal= {arXiv preprint arXiv:2603.21899},
year = {2026}
}