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Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations
Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations
- Source :
- BIRD: BCAM's Institutional Repository Data, instname
- Publication Year :
- 2012
-
Abstract
- This article is devoted to the analysis of the convergence rates of several numerical approximation schemes for linear and nonlinear Schrodinger equations on the real line. Recently, the authors have introduced viscous and two-grid numerical approximation schemes that mimic at the discrete level the so-called Strichartz dispersive estimates of the continuous Schrodinger equation. This allows to guarantee the convergence of numerical approximations for initial data in L 2 ( R ) , a fact that cannot be proved in the nonlinear setting for standard conservative schemes unless more regularity of the initial data is assumed. In the present article we obtain explicit convergence rates and prove that dispersive schemes fulfilling the Strichartz estimates are better behaved for H s ( R ) data if 0 s 1 / 2 . Indeed, while dispersive schemes ensure a polynomial convergence rate, non-dispersive ones only yield logarithmic ones.
- Subjects :
- Finite differences
Mathematics(all)
Polynomial
Applied Mathematics
General Mathematics
010102 general mathematics
Mathematical analysis
Finite difference
01 natural sciences
Schrödinger equation
010101 applied mathematics
Strichartz estimates
symbols.namesake
Nonlinear system
Rate of convergence
Error analysis
Convergence (routing)
symbols
Nonlinear Schrödinger equation
0101 mathematics
Real line
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- BIRD: BCAM's Institutional Repository Data, instname
- Accession number :
- edsair.doi.dedup.....1e0fce3a2fa4f24c92db99ba7571c3d6