Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913059951345664 |
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| author | Roque, Emmanuel Vallejo, José A |
| author_facet | Roque, Emmanuel Vallejo, José A |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_02604 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis Roque, Emmanuel Vallejo, José A Numerical Analysis 35-04, 35C10:65T40 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. |
| title | Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis |
| topic | Numerical Analysis 35-04, 35C10:65T40 |
| url | https://arxiv.org/abs/2004.02604 |