Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis
Numerical Analysis
2026-04-28 v2 Numerical Analysis
Abstract
We provide the details of an implementation of Fourier techniques for solving second-order linear partial differential equations (with constant coefficients) using a computer algebra system. The general Sturm-Liouville problem for the heat, wave and Laplace operators on the most common bounded domains is covered, as well as the general second-order linear parabolic equation with constant coefficients, which includes cases such as the convection-diffusion equation, by reduction to the heat equation.
Cite
@article{arxiv.2004.02604,
title = {Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis},
author = {Emmanuel Roque and José A Vallejo},
journal= {arXiv preprint arXiv:2004.02604},
year = {2026}
}
Comments
Second version. 22 pages, 6 figures