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NA

2007

2007

A least-squares spectral collocation method for the one-dimensional inviscid Burgers equation is proposed. This model problem shows the stability and high accuracy of these schemes for nonlinear hyperbolic scalar equations. Here we make use of a least-squares spectral approach which was already used in an earlier paper for discontinuous and singular perturbation problems [10] . The domain is decomposed in subintervals where continuity is enforced at the interfaces. Equal order polynomials are used on all subdomains. For the spectral collocation scheme Chebyshev polynomials are employed which allow the eﬃcient implementation with Fast Fourier Transforms (FFTs). The collocation conditions and the interface conditions lead to an overdetermined system which can be eﬃciently solved by least-squares. The solution technique will only involve symmetric positive deﬁnite linear systems. The scheme exhibits exponential convergence where the exact solution is smooth. In parts of the domain ...

Related Content

Added |
27 Dec 2010 |

Updated |
27 Dec 2010 |

Type |
Journal |

Year |
2007 |

Where |
NA |

Authors |
Wilhelm Heinrichs |

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