{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:40:51Z","timestamp":1776836451517,"version":"3.51.2"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2007,12,15]],"date-time":"2007-12-15T00:00:00Z","timestamp":1197676800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2008,2]]},"DOI":"10.1007\/s00211-007-0129-3","type":"journal-article","created":{"date-parts":[[2007,12,14]],"date-time":"2007-12-14T02:54:05Z","timestamp":1197600845000},"page":"557-570","source":"Crossref","is-referenced-by-count":27,"title":["Dimension splitting for evolution equations"],"prefix":"10.1007","volume":"108","author":[{"given":"Eskil","family":"Hansen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Ostermann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,12,15]]},"reference":[{"issue":"3","key":"129_CR1","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/s00211-002-0434-9","volume":"95","author":"S. Descombes","year":"2003","unstructured":"Descombes S. and Ribot M. (2003). Convergence of the Peaceman\u2013Rachford approximation for reaction\u2013diffusion systems. Numer. Math. 95(3): 503\u2013525","journal-title":"Numer. Math."},{"issue":"1","key":"129_CR2","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/S0021-7824(01)01216-8","volume":"81","author":"S. Descombes","year":"2002","unstructured":"Descombes S. and Schatzman M. (2002). Strang\u2019s formula for holomorphic semi-groups. J. Math. Pures Appl. 81(1): 93\u2013114","journal-title":"J. Math. Pures Appl."},{"key":"129_CR3","unstructured":"Faou, E.: Analysis of splitting methods for reaction\u2013diffusion problems in the light of stochastic calculus. Preprint (2007)"},{"issue":"1","key":"129_CR4","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s00233-006-0640-3","volume":"74","author":"I. Farag\u00f3","year":"2007","unstructured":"Farag\u00f3 I. and Havasi \u00c1. (2007). Consistency analysis of operator splitting methods for C 0-semigroups. Semigroup Forum 74(1): 125\u2013139","journal-title":"Semigroup Forum"},{"issue":"4","key":"129_CR5","doi-asserted-by":"crossref","first-page":"1070","DOI":"10.1137\/S0036141003437903","volume":"37","author":"I. Gy\u00f6ngy","year":"2005","unstructured":"Gy\u00f6ngy I. and Krylov N. (2005). An accelerated splitting-up method for parabolic equations. SIAM J. Math. Anal. 37(4): 1070\u20131097","journal-title":"SIAM J. Math. Anal."},{"key":"129_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-09017-6","volume-title":"Numerical Solution of Time-Dependent Advection\u2013Diffusion\u2013Reaction Equations","author":"W. Hundsdorfer","year":"2003","unstructured":"Hundsdorfer W. and Verwer J. (2003). Numerical Solution of Time-Dependent Advection\u2013Diffusion\u2013Reaction Equations. Springer, Berlin"},{"key":"129_CR7","unstructured":"Ichinose, T., Tamura, H.: The norm convergence of the Trotter\u2013Kato product formula with error bound. Comm. Math. Phys. 217(3), 489\u2013502 (2001). Erratum: Comm. Math. Phys. 254(1), 255 (2005)"},{"issue":"4","key":"129_CR8","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1023\/A:1022396519656","volume":"40","author":"T. Jahnke","year":"2000","unstructured":"Jahnke T. and Lubich C. (2000). Error bounds for exponential operator splittings. BIT 40(4): 735\u2013744","journal-title":"BIT"},{"key":"129_CR9","volume-title":"Weighted Sobolev Spaces","author":"A. Kufner","year":"1985","unstructured":"Kufner A. (1985). Weighted Sobolev Spaces. Wiley, New York"},{"issue":"12","key":"129_CR10","doi-asserted-by":"crossref","first-page":"3569","DOI":"10.1090\/S0002-9939-01-06034-8","volume":"129","author":"F. K\u00fchnemund","year":"2001","unstructured":"K\u00fchnemund F. and Wacker M. (2001). Commutator conditions implying the convergence of the Lie\u2013Trotter products. Proc. Am. Math. Soc. 129(12): 3569\u20133582","journal-title":"Proc. Am. Math. Soc."},{"key":"129_CR11","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1017\/S0962492902000053","volume":"11","author":"R.I. McLachlan","year":"2002","unstructured":"McLachlan R.I. and Quispel G.R.W. (2002). Splitting methods. Acta Numer. 11: 341\u2013434","journal-title":"Acta Numer."},{"issue":"1","key":"129_CR12","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s002200050671","volume":"205","author":"H. Neidhardt","year":"1999","unstructured":"Neidhardt H. and Zagrebnov V.A. (1999). Trotter\u2013Kato product formula and operator-norm convergence. Comm. Math. Phys. 205(1): 129\u2013159","journal-title":"Comm. Math. Phys."},{"key":"129_CR13","doi-asserted-by":"crossref","first-page":"258","DOI":"10.1002\/mana.3210040124","volume":"4","author":"J. Neumann von","year":"1951","unstructured":"von Neumann J. (1951). Eine Spektraltheorie f\u00fcr allgemeine Operatoren eines unit\u00e4ren Raumes. Math. Nachr. 4: 258\u2013281","journal-title":"Math. Nachr."},{"issue":"1\u20133","key":"129_CR14","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/S0168-9274(01)00160-X","volume":"42","author":"A. Ostermann","year":"2002","unstructured":"Ostermann A. (2002). Stability of W-methods with applications to operator splitting and to geometric theory. Appl. Numer. Math. 42(1\u20133): 353\u2013366","journal-title":"Appl. Numer. Math."},{"key":"129_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5561-1","volume-title":"Semigroups of Linear Operators and Applications to Partial Differential Equations","author":"A. Pazy","year":"1983","unstructured":"Pazy A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York"},{"key":"129_CR16","first-page":"1","volume":"20","author":"S. Rasmussen","year":"1972","unstructured":"Rasmussen S. (1972). Non-linear semi-groups, evolution equations and productintegral representations. Various publications series, Aarhus University 20: 1\u201389","journal-title":"Various publications series, Aarhus University"},{"issue":"1","key":"129_CR17","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1006\/jfan.1998.3311","volume":"162","author":"M. Schatzman","year":"1999","unstructured":"Schatzman M. (1999). Stability of the Peaceman\u2013Rachford approximation. J. Funct. Anal. 162(1): 219\u2013255","journal-title":"J. Funct. Anal."},{"key":"129_CR18","volume-title":"Interpolation Theory, Function Spaces, Differential Operators","author":"H. Triebel","year":"1978","unstructured":"Triebel H. (1978). Interpolation Theory, Function Spaces, Differential Operators. North-Holland, Amsterdam"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0129-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-007-0129-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0129-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T12:22:40Z","timestamp":1558614160000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-007-0129-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12,15]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["129"],"URL":"https:\/\/doi.org\/10.1007\/s00211-007-0129-3","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12,15]]}}}