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Scattering and Uniform in Time Error Estimates for Splitting Method in NLS

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Abstract

We consider the nonlinear Schrödinger equation with a defocusing nonlinearity which is mass-(super)critical and energy-subcritical. We prove uniform in time error estimates for the Lie–Trotter time splitting discretization. This uniformity in time is obtained thanks to a vectorfield which provides time decay estimates for the exact and numerical solutions. This vectorfield is classical in scattering theory and requires several technical modifications compared to previous error estimates for splitting methods.

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Authors and Affiliations

  1. CNRS IRMAR - UMR 6625, Univ Rennes, 35000, Rennes, France

    Rémi Carles

  2. Yau Mathematical Sciences Center, Tsinghua University, 10084, Beijing, China

    Chunmei Su

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  1. Rémi Carles
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  2. Chunmei Su
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Correspondence to Chunmei Su.

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Communicated by Christian Lubich.

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RC was supported by Rennes Métropole through its AIS program and by Centre Henri Lebesgue, program ANR-11-LABX-0020-0.

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Carles, R., Su, C. Scattering and Uniform in Time Error Estimates for Splitting Method in NLS. Found Comput Math 24, 683–722 (2024). https://doi.org/10.1007/s10208-022-09600-9

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