| 摘要: |
| 在本文中，我们提出了两种谱方法，为在无界区域上求解具有爆破现象的偏微分方程提供了更多的选择。一种是基于映射的谱方法，与传统的将无限区间映射到有限区间的经典映射技术不同，我们发现一种映射可以将无界区间映射到自身，并将正交基函数的根集中在爆破点附近。另一种是自适应映射谱方法，该方法类似于 Xia Mingtao, Shao Sihong, Chou(2021)的工作。此外，我们给出了这两种方法的误差估计，并提供了数值算例验证其有效性。 |
| 关键词: 爆破型方程 映射谱方法 自适应映射谱方法 |
| DOI： |
| 分类号:O241.82 |
| 基金项目:国家青年自然科学基金 |
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| Spectral methods for solving blow-up PDEs on an unbounded domain |
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Shi Jinxin, Shen Shengyi
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| Abstract: |
| In this paper, we propose two spectral methods that provide additional options for solving partial differential equations with blow-up phenomena on unbounded domains. The first is a mapping-based spectral method; unlike traditional mapping techniques that transform infinite intervals into finite ones, we identify a mapping that maps an unbounded interval onto itself and concentrates the roots of the orthogonal basis functions near the blow-up point. The second is an adaptive mapping spectral method, which is similar to the work of Xia, Shao, and Chou (2021). Furthermore, error estimates for both methods are provided, along with numerical examples to verify their effectiveness. |
| Key words: blow-up equation, mapped spectral method, adaptive mapped spectral method |
