Abstract
In this paper, we propose an embedded low-regularity integrator (ELRI) under a new framework for solving the modified Korteweg-de Vries (mKdV) equation under rough data. Different from the previous work [Wu and Zhao, BIT, Number. Math., (2021)], the present ELRI scheme is constructed based on an approximation of a scaled Schrödinger operator and a new strategy of iterative regularizing through the inverse Miura transform. Moreover, the ELRI scheme is explicitly defined in the physical space, and it is efficient under the Fourier pseudospectral discretization. By rigorous error analysis, we show that ELRI achieves first-order accuracy by requiring the boundedness of one additional spatial derivative of the solution. Numerical results are presented to show the accuracy and efficiency of ELRI.
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