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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 numerical evidence supports the validity of the $\\log \\log$ law $[\\ln\\ln \\frac {1}{t^\\star -t} \/(t^\\star-t)]^{1\/2}$ 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 $t\\to t^\\star.$<\/jats:p>","DOI":"10.1137\/s1064827597332041","type":"journal-article","created":{"date-parts":[[2003,11,7]],"date-time":"2003-11-07T11:17:43Z","timestamp":1068203863000},"page":"186-212","source":"Crossref","is-referenced-by-count":28,"title":["Numerical Approximation of Blow-Up of Radially Symmetric Solutions of the Nonlinear Schr\u00f6dinger Equation"],"prefix":"10.1137","volume":"25","author":[{"given":"G. D.","family":"Akrivis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V. A.","family":"Dougalis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"O. 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