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Error estimates at low regularity of splitting schemes for NLS
- Source :
- Mathematics of Computation
- Publication Year :
- 2021
- Publisher :
- American Mathematical Society (AMS), 2021.
-
Abstract
- We study a filtered Lie splitting scheme for the cubic nonlinear Schrödinger equation. We establish error estimates at low regularity by using discrete Bourgain spaces. This allows us to handle data in H s H^s with 0 > s > 1 0>s>1 overcoming the standard stability restriction to smooth Sobolev spaces with index s > 1 / 2 s>1/2 . More precisely, we prove convergence rates of order τ s / 2 \tau ^{s/2} in L 2 L^2 at this level of regularity.
- Subjects :
- Algebra and Number Theory
Applied Mathematics
Order (ring theory)
Numerical Analysis (math.NA)
010103 numerical & computational mathematics
01 natural sciences
010101 applied mathematics
Computational Mathematics
symbols.namesake
Scheme (mathematics)
Convergence (routing)
FOS: Mathematics
symbols
Applied mathematics
Mathematics - Numerical Analysis
0101 mathematics
Nonlinear Schrödinger equation
Mathematics
Subjects
Details
- ISSN :
- 10886842 and 00255718
- Volume :
- 91
- Database :
- OpenAIRE
- Journal :
- Mathematics of Computation
- Accession number :
- edsair.doi.dedup.....53a0e002df8cb178abf8a42658f1dc20