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Register a new userA fully discrete low-regularity integrator for the nonlinear Schrodinger equation
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Added by
Fangyan Yao
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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For the solution of the cubic nonlinear Schrodinger equation in one space dimension, we propose and analyse a fully discrete low-regularity integrator. The scheme is explicit and can easily be implemented using the fast Fourier transform with a complexity of $mathcal{O}(Nlog N)$ operations per time step, where $N$ denotes the degrees of freedom in the spatial discretisation. We prove that the new scheme provides an $mathcal{O}(tau^{frac32gamma-frac12-varepsilon}+N^{-gamma})$ error bound in $L^2$ for any initial data belonging to $H^gamma$, $frac12<gammaleq 1$, where $tau$ denotes the temporal step size. Numerical examples illustrate this convergence behavior.
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