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A fast solver of Legendre-Laguerre spectral element method for the Camassa-Holm equation

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Abstract

An efficient and accurate Legendre-Laguerre spectral element method for solving the Camassa-Holm equation on the half line is proposed. The spectral element method has the flexibility for arbitrary h and p adaptivity. Two kinds of Sobolev orthogonal basis functions corresponding to each subinterval are constructed, which reduces the non-zero entries of linear systems and computational cost. Numerical experiments illustrate the effectiveness and accuracy of the suggested approach.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 12071294).

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  1. University of Shanghai for Science and Technology, Shanghai, 200093, China

    Xuhong Yu, Xueqin Ye & Zhongqing Wang

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  1. Xuhong Yu
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  2. Xueqin Ye
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  3. Zhongqing Wang
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Correspondence to Zhongqing Wang.

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Yu, X., Ye, X. & Wang, Z. A fast solver of Legendre-Laguerre spectral element method for the Camassa-Holm equation. Numer Algor 88, 1–23 (2021). https://doi.org/10.1007/s11075-020-01028-y

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