Long-time behavior of multi-step Finite Difference schemes with boundary via steepest descent and analytic combinatorics

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.

Source: arXiv:2603.21899v1 - http://arxiv.org/abs/2603.21899v1 PDF: https://arxiv.org/pdf/2603.21899v1 Original Link: http://arxiv.org/abs/2603.21899v1