Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis
This work provides an automated tool for solving a class of PDEs, which is useful for educators and practitioners, but the approach is a straightforward application of existing Fourier methods.
The paper presents a computer algebra implementation for solving constant-coefficient second-order linear PDEs using Fourier analysis, covering Sturm-Liouville problems for heat, wave, and Laplace operators on bounded domains, and reducing general parabolic equations to the heat equation.
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.