A quantum graph FFT with applications to partial differential equations on networks
Numerical Analysis
2025-07-11 v2 Numerical Analysis
Abstract
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial differential equations on domains which are modeled as networks of one dimensional segments joined at nodes.
Cite
@article{arxiv.2410.19969,
title = {A quantum graph FFT with applications to partial differential equations on networks},
author = {Robert Carlson},
journal= {arXiv preprint arXiv:2410.19969},
year = {2025}
}
Comments
The new version includes a pseudospectral algorithm. Examples are limited to the Schrodinger equation to highlight the advantages of spectral and pseudospectral methods