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A TVD Type Wavelet-Galerkin Method for Hamilton-Jacobi Equations

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Abstract

In this paper, we use Daubechies scaling functions as test functions for the Galerkin method, and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations. It can be proved that the schemes are TVD schemes. Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations. Furthermore, they have high-order accuracy in smooth regions and good resolution of singularities.

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Authors and Affiliations

  1. Department of Mathematics and System Science, Science School, National University of Defense Technology, Hunan, 410073, China

    Ling-yan Tang & Song-he Song

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  1. Ling-yan Tang
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  2. Song-he Song
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Correspondence to Ling-yan Tang.

Additional information

Supported by the National Natural Science Foundation of China (No. 10571178).

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Tang, Ly., Song, Sh. A TVD Type Wavelet-Galerkin Method for Hamilton-Jacobi Equations. Acta Mathematicae Applicatae Sinica, English Series 23, 303–310 (2007). https://doi.org/10.1007/s10255-007-0372-5

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  • DOI: https://doi.org/10.1007/s10255-007-0372-5

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