论文标题
使用傅立叶分析自动求解恒定的二阶线性PDE
Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis
论文作者
论文摘要
在讨论了当前商业软件的局限性之后，我们提供了实现傅立叶技术的详细信息，以求解使用计算机代数系统的二阶线性偏微分方程（具有恒定系数）。涵盖了最常见的有界结构域上的热，波和拉普拉斯操作员的一般sturm-liouville问题，以及具有恒定系数的一般二阶线性抛物线方程，其中包括通过还原到热方程来诸如对流 - 扩散方程的案例。
After discussing the limitations of current commercial software, 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.
