Polynomial Approximation of Differential Equations
Polynomial Approximation of Differential Equations
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DOI：
10.1007/978-3-540-46783-0
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发表时间：
1992-05
期刊：
影响因子：
--
通讯作者：
D. Funaro
中科院分区：
文献类型：
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作者：
D. Funaro
这本书致力于分析微分方程的近似解技术，基于经典的正交多项式。这些技术通常被称为光谱方法。在过去的几十年里，人们对这个问题越来越感兴趣。事实上，谱方法为各种各样的问题提供了一种与其他标准近似技术相比具有竞争力的替代方法。初步应用是用三角多项式研究边值问题的周期解。随后，分析扩展到代数多项式。正交基函数的展开式由于其计算的高精度和灵活性而受到青睐。这本书的目的是提出一个初步的数学背景是ginners谁希望研究和执行数值实验，或谁希望提高自己的技能，以解决更具体的应用。此外，它还提供了一个基本公式和定理的综合集合，这些公式和定理对任何复杂程度的实现都很有用。我们试图保持一个基本的阐述，这样就不需要函数分析的经验。
This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods. In the last few decades, there has been a growing interest in this subject. As a matter offact, spectral methods provide a competitive alternative to other standard approximation techniques, for a large variety of problems. Initial ap plications were concerned with the investigation of periodic solutions of boundary value problems using trigonometric polynomials. Subsequently, the analysis was extended to algebraic polynomials. Expansions in orthogonal basis functions were preferred, due to their high accuracy and flexibility in computations. The aim of this book is to present a preliminary mathematical background for be ginners who wish to study and perform numerical experiments, or who wish to improve their skill in order to tackle more specific applications. In addition, it furnishes a com prehensive collection of basic formulas and theorems that are useful for implementations at any level of complexity. We tried to maintain an elementary exposition so that no experience in functional analysis is required.