Machine learningHigh-Order Projection
谱方法
谱方法是求解微分方程的高阶数值技术，它使用全局多项式展开（例如傅里叶级数或勒让德级数）而非局部分段多项式。该方法由Steven Orszag于20世纪60年代为湍流模拟而开发，对于光滑问题具有指数收敛性，因此非常适合于解的正则性很高的科学计算。
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来源
- Orszag, S. A. (1969). Numerical methods for the simulation of turbulence. Physics of Fluids Supplements, 12(12), 250–257. DOI: 10.1063/1.1692445 ↗
- Gottlieb, D., & Orzag, S. A. (1977). Numerical Analysis of Spectral Methods: Theory and Applications. SIAM. DOI: 10.1137/1.9781611970425 ↗
- Canuto, C., Hussaini, M. Y., Quarteroni, A., & Zang, T. A. (2006). Spectral Methods: Fundamentals in Single Domains. Springer. DOI: 10.1007/978-3-540-30726-6 ↗
如何引用本页
ScholarGate. (2026, June 3). Spectral Methods for Differential Equations. ScholarGate. https://scholargate.app/zh/numerical-methods/spectral-methods
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