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An exponential integrator sine pseudospectral method for the generalized improved Boussinesq equation

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Abstract

A Deuflhard-type exponential integrator sine pseudospectral (DEI-SP) method is proposed and analyzed for solving the generalized improved Boussinesq (GIBq) equation. The numerical scheme is based on a second-order exponential integrator for time integration and a sine pseudospectral discretization in space. Rigorous analysis and abundant experiments show that the method converges quadratically and spectrally in time and space, respectively. Finally the DEI-SP method is applied to investigate the complicated and interesting long-time dynamics of the GIBq equation.

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Acknowledgements

C. Su is supported by the Alexander von Humboldt Foundation. C. Su would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme Geometry, compatibility and structure preservation in computational differential equations when work on this paper was taken. The second author would like to thank Dr. Ali Shokri for helpful communication.

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Authors and Affiliations

  1. Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

    Chunmei Su

  2. Zentrum Mathematik, Technische Universität München, 85748, Garching bei München, Germany

    Chunmei Su

  3. Department of Mathematics, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey

    Gulcin M. Muslu

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  1. Chunmei Su
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  2. Gulcin M. Muslu
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Correspondence to Gulcin M. Muslu.

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Communicated by Christian Lubich.

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Su, C., Muslu, G.M. An exponential integrator sine pseudospectral method for the generalized improved Boussinesq equation. Bit Numer Math 61, 1397–1419 (2021). https://doi.org/10.1007/s10543-021-00865-0

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