Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schrodinger equation
| dc.contributor.author | Akrivis, G. D. | en |
| dc.contributor.author | Dougalis, V. A. | en |
| dc.contributor.author | Karakashian, O. A. | en |
| dc.contributor.author | McKinney, W. R. | en |
| dc.date.accessioned | 2015-11-24T17:00:20Z | |
| dc.date.available | 2015-11-24T17:00:20Z | |
| dc.identifier.issn | 1064-8275 | - |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/10750 | |
| dc.rights | Default Licence | - |
| dc.subject | nonlinear schrodinger equation | en |
| dc.subject | point blow-up | en |
| dc.subject | finite element methods | en |
| dc.subject | adaptive mesh refinement | en |
| dc.subject | self-focusing singularity | en |
| dc.subject | critical dimension | en |
| dc.subject | cauchy-problem | en |
| dc.subject | simulation | en |
| dc.subject | collapse | en |
| dc.subject | media | en |
| dc.subject | beams | en |
| dc.title | Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schrodinger equation | en |
| heal.abstract | We consider the initial-value problem for the radially symmetric nonlinear Schrodinger equation with cubic nonlinearity (NLS) in d = 2 and 3 space dimensions. To approximate smooth solutions of this problem, we construct and analyze a numerical method based on a standard Galerkin finite element spatial discretization with piecewise linear, continuous functions and on an implicit Crank-Nicolson type time-stepping procedure. We then equip this scheme with an adaptive spatial and temporal mesh refinement mechanism that enables the numerical technique to approximate well singular solutions of the NLS equation that blow up at the origin as the temporal variable t tends from below to a finite value t(star). For the blow-up of the amplitude of the solution we recover numerically the well-known rate (t(star)- t)(-1/2) for d = 3. For d = 2 our numericalevidence supports the validity of the log log law [ln ln 1/t(star)-t/(t(star)- t)](1/2) for t extremely close to t(star). The scheme also approximates well the details of the blow-up of the phase of the solution at the origin as t --> t(star). | en |
| heal.access | campus | - |
| heal.fullTextAvailability | TRUE | - |
| heal.identifier.primary | Doi 10.1137/S1064827597332041 | - |
| heal.journalName | Siam Journal on Scientific Computing | en |
| heal.journalType | peer reviewed | - |
| heal.language | en | - |
| heal.publicationDate | 2003 | - |
| heal.recordProvider | Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μηχανικών Ηλεκτρονικών Υπολογιστών και Πληροφορικής | el |
| heal.type | journalArticle | - |
| heal.type.el | Άρθρο Περιοδικού | el |
| heal.type.en | Journal article | en |
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