用谱方法近似求解双曲型偏微分方程
Using Spectral Method as an Approximation for Solving Hyperbolic PDEs
摘要：
我们展示了一个应用程序的谱方法作为一个数值逼近求解双曲偏微分方程。在该方法中，有限基用于近似解。特别是，我们证明了一组这样的解决方案的情况下，否则几乎不可能解决的更常规的方法，如有限差分法。特征值问题包括在这类偏微分方程的方法是可解的。虽然可以使用任何完整的正交基，我们讨论两个特别有趣的基础：傅立叶基础和量子振子本征函数基础。我们比较和讨论这两个基地的相对优势。
英文摘要：
We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for cases which would be otherwise almost impossible to solve by the more routine methods such as the Finite Difference Method. Eigenvalue problems are included in the class of PDEs that are solvable by this method. Although any complete orthonormal basis can be used, we discuss two particularly interesting bases: the Fourier basis and the quantum oscillator eigenfunction basis. We compare and discuss the relative advantages of each of these two bases.
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