Using Spectral Method as an Approximation for Solving Hyperbolic PDEs

Details Using Spectral Method as an Approximation for Solving Hyperbolic PDEs Using Spectral Method as an Approximation for Solving Hyperbolic PDEs

2007-01-05

arxiv.org/abs/math-ph/0701015v2

Comput.Phys.Commun.176:581-588,2007

Physics

Mathematical Physics

19 pages, 14 figures. to appear in Computer Physics Communication

Scientific paper

10.1016/j.cpc.2007.01.004

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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