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A New Multi-Domain Spectral Method for Korteweg-de Vries Equation on The Whole Line

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Abstract

Some composite generalized Laguerre-Legendre quasi-orthogonal approximation results on the whole line are established. A novel multi-domain composite generalized Laguerre-Legendre spectral scheme is provided for the Korteweg-de Vries equation on the whole line. The scheme features mobile common boundaries of the adjacent subdomains, which better fits the soliton wave governed by the Korteweg-de Vries equation. Convergence of the proposed scheme is proved. Numerical results show the efficiency of the scheme and coincide well with theoretical analysis.

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Acknowledgements

The authors would like to thank the anonymous referees, Dr. Yue Zhu of Hangzhou Dianzi University and Dr. Lu-yu Wang of Zhejiang University for their help on polishing this work.

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  1. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471003, China

    Tian-jun Wang

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  1. Tian-jun Wang
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Tian-jun Wang is supported in part by NSF of China [grant numbers 12171141, 11371123] and NSF of Henan Province [grant numbers 202300410156]

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Wang, Tj. A New Multi-Domain Spectral Method for Korteweg-de Vries Equation on The Whole Line. J Sci Comput 92, 32 (2022). https://doi.org/10.1007/s10915-022-01887-8

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