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- W4302088892 abstract "In this paper, we establish a convergence result for the operator splitting scheme $Z_{tau}$ introduced by Ignat, with initial data in $H^1$, for the nonlinear Schrodinger equation : $$ partial_t u = i Delta u + ilambda |u|^{p} u,qquad u (x,0) =phi (x), $$ where $(x,t) in mathbb{R}^d times [0,infty)$, with $0< p < 4/(d-2)$ for $dgeq3$ and $0< p<infty$ for $d=1,2$. We prove the $L^2$ convergence of order $mathcal{O}(tau^{1/2})$ for this scheme with initial data in the space $H^1 (mathbb{R}^d)$." @default.
- W4302088892 created "2022-10-06" @default.
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- W4302088892 date "2016-10-19" @default.
- W4302088892 modified "2023-10-01" @default.
- W4302088892 title "On the splitting method for the nonlinear Schrodinger equation with initial data in $H^1$" @default.
- W4302088892 doi "https://doi.org/10.48550/arxiv.1610.06028" @default.
- W4302088892 hasPublicationYear "2016" @default.
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