{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T16:13:59Z","timestamp":1781712839052,"version":"3.54.5"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,7,15]],"date-time":"2019-07-15T00:00:00Z","timestamp":1563148800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,7,15]],"date-time":"2019-07-15T00:00:00Z","timestamp":1563148800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2019,10]]},"DOI":"10.1007\/s00211-019-01058-2","type":"journal-article","created":{"date-parts":[[2019,7,15]],"date-time":"2019-07-15T11:04:38Z","timestamp":1563188678000},"page":"461-487","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["Regularized numerical methods for the logarithmic Schr\u00f6dinger equation"],"prefix":"10.1007","volume":"143","author":[{"given":"Weizhu","family":"Bao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R\u00e9mi","family":"Carles","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chunmei","family":"Su","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qinglin","family":"Tang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,7,15]]},"reference":[{"issue":"1","key":"1058_CR1","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1093\/imanum\/13.1.115","volume":"13","author":"GD Akrivis","year":"1993","unstructured":"Akrivis, G.D.: Finite difference discretization of the cubic Schr\u00f6dinger equation. IMA J. Numer. Anal. 13(1), 115\u2013124 (1993)","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"1058_CR2","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/BF01385769","volume":"59","author":"GD Akrivis","year":"1991","unstructured":"Akrivis, G.D., Dougalis, V.A., Karakashian, O.A.: On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schr\u00f6dinger equation. Numer. Math. 59(1), 31\u201353 (1991)","journal-title":"Numer. Math."},{"key":"1058_CR3","doi-asserted-by":"publisher","first-page":"2621","DOI":"10.1016\/j.cpc.2013.07.012","volume":"184","author":"X Antoine","year":"2013","unstructured":"Antoine, X., Bao, W., Besse, C.: Computational methods for dynamics of the nonlinear Schr\u00f6dinger\/Gross\u2013Pitaevskii equations. Comput. Phys. Commun. 184, 2621\u20132633 (2013)","journal-title":"Comput. Phys. Commun."},{"key":"1058_CR4","first-page":"1","volume":"335","author":"AH Ardila","year":"2016","unstructured":"Ardila, A.H.: Orbital stability of Gausson solutions to logarithmic Schr\u00f6dinger equations. Electron. J. Differ. Eq. 335, 1\u20139 (2016)","journal-title":"Electron. J. Differ. Eq."},{"issue":"19","key":"1058_CR5","doi-asserted-by":"publisher","first-page":"195303","DOI":"10.1088\/0953-4075\/44\/19\/195303","volume":"44","author":"AV Avdeenkov","year":"2011","unstructured":"Avdeenkov, A.V., Zloshchastiev, K.G.: Quantum Bose liquids with logarithmic nonlinearity: self-sustainability and emergence of spatial extent. J. Phys. B: Atomic Mol. Opt. Phys. 44(19), 195303 (2011)","journal-title":"J. Phys. B: Atomic Mol. Opt. Phys."},{"issue":"2","key":"1058_CR6","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1137\/110830800","volume":"50","author":"W Bao","year":"2012","unstructured":"Bao, W., Cai, Y.: Uniform error estimates of finite difference methods for the nonlinear Schr\u00f6dinger equation with wave operator. SIAM J. Numer. Anal. 50(2), 492\u2013521 (2012)","journal-title":"SIAM J. Numer. Anal."},{"issue":"281","key":"1058_CR7","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1090\/S0025-5718-2012-02617-2","volume":"82","author":"W Bao","year":"2013","unstructured":"Bao, W., Cai, Y.: Optimal error estimates of finite difference methods for the Gross\u2013Pitaevskii equation with angular momentum rotation. Math. Comp. 82(281), 99\u2013128 (2013)","journal-title":"Math. Comp."},{"issue":"2","key":"1058_CR8","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1137\/18M1177445","volume":"57","author":"W Bao","year":"2019","unstructured":"Bao, W., Carles, R., Su, C., Tang, Q.: Error estimates of a regularized finite difference method for the logarithmic Schr\u00f6dinger equation. SIAM J. Numer. Anal. 57(2), 657\u2013680 (2019)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1058_CR9","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1016\/S0021-9991(03)00102-5","volume":"187","author":"W Bao","year":"2003","unstructured":"Bao, W., Jaksch, D., Markowich, P.A.: Numerical solution of the Gross\u2013Pitaevskii equation for Bose\u2013Einstein condensation. J. Comput. Phys. 187(1), 318\u2013342 (2003)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1058_CR10","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1006\/jcph.2001.6956","volume":"175","author":"W Bao","year":"2002","unstructured":"Bao, W., Jin, S., Markowich, P.A.: On time-splitting spectral approximations for the Schr\u00f6dinger equation in the semiclassical regime. J. Comput. Phys. 175(2), 487\u2013524 (2002)","journal-title":"J. Comput. Phys."},{"key":"1058_CR11","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1016\/j.jcp.2012.10.054","volume":"235","author":"W Bao","year":"2013","unstructured":"Bao, W., Tang, Q., Xu, Z.: Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schr\u00f6dinger equation. J. Comput. Phys. 235, 423\u2013445 (2013)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"1058_CR12","doi-asserted-by":"publisher","first-page":"934","DOI":"10.1137\/S0036142901396521","volume":"42","author":"C Besse","year":"2004","unstructured":"Besse, C.: A relaxation scheme for the nonlinear Schr\u00f6dinger equation. SIAM J. Numer. Anal. 42(3), 934\u2013952 (2004)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1058_CR13","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1137\/S0036142900381497","volume":"40","author":"C Besse","year":"2002","unstructured":"Besse, C., Bid\u00e9garay, B., Descombes, S.: Order estimates in time of splitting methods for the nonlinear Schr\u00f6dinger equation. SIAM J. Numer. Anal. 40(1), 26\u201340 (2002)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1\u20132","key":"1058_CR14","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/0003-4916(76)90057-9","volume":"100","author":"I Bia\u0142ynicki-Birula","year":"1976","unstructured":"Bia\u0142ynicki-Birula, I., Mycielski, J.: Nonlinear wave mechanics. Ann. Phys. 100(1\u20132), 62\u201393 (1976)","journal-title":"Ann. Phys."},{"key":"1058_CR15","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1088\/0031-8949\/20\/3-4\/033","volume":"20","author":"I Bia\u0142ynicki-Birula","year":"1979","unstructured":"Bia\u0142ynicki-Birula, I., Mycielski, J.: Gaussons: solitons of the logarithmic Schr\u00f6dinger equation. Special issue on solitons in physics. Phys. Scr. 20, 539\u2013544 (1979)","journal-title":"Phys. Scr."},{"issue":"3","key":"1058_CR16","doi-asserted-by":"publisher","first-page":"036607","DOI":"10.1103\/PhysRevE.68.036607","volume":"68","author":"H Buljan","year":"2003","unstructured":"Buljan, H., \u0160iber, A., Solja\u010di\u0107, M., Schwartz, T., Segev, M., Christodoulides, D.: Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media. Phys. Rev. E 68(3), 036607 (2003)","journal-title":"Phys. Rev. E"},{"issue":"6","key":"1058_CR17","doi-asserted-by":"publisher","first-page":"3232","DOI":"10.1137\/120892416","volume":"51","author":"R Carles","year":"2013","unstructured":"Carles, R.: On Fourier time-splitting methods for nonlinear Schr\u00f6dinger equations in the semiclassical limit. SIAM J. Numer. Anal. 51(6), 3232\u20133258 (2013)","journal-title":"SIAM J. Numer. Anal."},{"issue":"9","key":"1058_CR18","doi-asserted-by":"publisher","first-page":"1761","DOI":"10.1215\/00127094-2018-0006","volume":"167","author":"R Carles","year":"2018","unstructured":"Carles, R., Gallagher, I.: Universal dynamics for the defocusing logarithmic Schr\u00f6dinger equation. Duke Math. J. 167(9), 1761\u20131801 (2018)","journal-title":"Duke Math. J."},{"issue":"1","key":"1058_CR19","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s00211-016-0841-y","volume":"136","author":"R Carles","year":"2017","unstructured":"Carles, R., Gallo, C.: On Fourier time-splitting methods for nonlinear Schr\u00f6dinger equations in the semi-classical limit II. Anal. Regul. Numer. Math. 136(1), 315\u2013342 (2017)","journal-title":"Anal. Regul. Numer. Math."},{"issue":"10","key":"1058_CR20","doi-asserted-by":"publisher","first-page":"1127","DOI":"10.1016\/0362-546X(83)90022-6","volume":"7","author":"T Cazenave","year":"1983","unstructured":"Cazenave, T.: Stable solutions of the logarithmic Schr\u00f6dinger equation. Nonlinear Anal. 7(10), 1127\u20131140 (1983)","journal-title":"Nonlinear Anal."},{"key":"1058_CR21","doi-asserted-by":"crossref","unstructured":"Cazenave, T.: Semilinear Schr\u00f6dinger equations, Courant Lecture Notes in Mathematics, vol. 10. New York University Courant Institute of Mathematical Sciences, New York (2003)","DOI":"10.1090\/cln\/010"},{"issue":"1","key":"1058_CR22","doi-asserted-by":"publisher","first-page":"21","DOI":"10.5802\/afst.543","volume":"2","author":"T Cazenave","year":"1980","unstructured":"Cazenave, T., Haraux, A.: \u00c9quations d\u2019\u00e9volution avec non lin\u00e9arit\u00e9 logarithmique. Ann. Fac. Sci. Toulouse Math. (5) 2(1), 21\u201351 (1980)","journal-title":"Ann. Fac. Sci. Toulouse Math. (5)"},{"issue":"4","key":"1058_CR23","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/BF01403504","volume":"85","author":"T Cazenave","year":"1982","unstructured":"Cazenave, T., Lions, P.L.: Orbital stability of standing waves for some nonlinear Schr\u00f6dinger equations. Commun. Math. Phys. 85(4), 549\u2013561 (1982)","journal-title":"Commun. Math. Phys."},{"issue":"2","key":"1058_CR24","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1006\/jcph.1998.6120","volume":"148","author":"Q Chang","year":"1999","unstructured":"Chang, Q., Jia, E., Sun, W.: Difference schemes for solving the generalized nonlinear Schr\u00f6dinger equation. J. Comput. Phys. 148(2), 397\u2013415 (1999)","journal-title":"J. Comput. Phys."},{"issue":"5","key":"1058_CR25","doi-asserted-by":"publisher","first-page":"3705","DOI":"10.1137\/080744578","volume":"47","author":"A Debussche","year":"2009","unstructured":"Debussche, A., Faou, E.: Modified energy for split-step methods applied to the linear Schr\u00f6dinger equation. SIAM J. Numer. Anal. 47(5), 3705\u20133719 (2009)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"1058_CR26","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1093\/imanum\/drs021","volume":"33","author":"S Descombes","year":"2012","unstructured":"Descombes, S., Thalhammer, M.: The Lie\u2013Trotter splitting for nonlinear evolutionary problems with critical parameters: a compact local error representation and application to nonlinear Schr\u00f6dinger equations in the semiclassical regime. IMA J. Numer. Anal. 33(2), 722\u2013745 (2012)","journal-title":"IMA J. Numer. Anal."},{"issue":"4","key":"1058_CR27","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/s10208-011-9094-4","volume":"11","author":"E Faou","year":"2011","unstructured":"Faou, E., Gr\u00e9bert, B.: Hamiltonian interpolation of splitting approximations for nonlinear PDEs. Found. Comput. Math. 11(4), 381\u2013415 (2011)","journal-title":"Found. Comput. Math."},{"issue":"3","key":"1058_CR28","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/s10208-010-9063-3","volume":"10","author":"L Gauckler","year":"2010","unstructured":"Gauckler, L., Lubich, C.: Splitting integrators for nonlinear Schr\u00f6dinger equations over long times. Found. Comput. Math. 10(3), 275\u2013302 (2010)","journal-title":"Found. Comput. Math."},{"issue":"197","key":"1058_CR29","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1090\/S0025-5718-1992-1106968-6","volume":"58","author":"R Glassey","year":"1992","unstructured":"Glassey, R.: Convergence of an energy-preserving scheme for the Zakharov equations in one space dimension. Math. Comp. 58(197), 83\u2013102 (1992)","journal-title":"Math. Comp."},{"issue":"1","key":"1058_CR30","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.nonrwa.2008.10.017","volume":"11","author":"P Guerrero","year":"2010","unstructured":"Guerrero, P., L\u00f3pez, J.L., Nieto, J.: Global $$H^1$$ solvability of the 3D logarithmic Schr\u00f6dinger equation. Nonlinear Anal. Real World Appl. 11(1), 79\u201387 (2010)","journal-title":"Nonlinear Anal. Real World Appl."},{"issue":"2","key":"1058_CR31","first-page":"121","volume":"4","author":"B Guo","year":"1986","unstructured":"Guo, B.: The convergence of numerical method for nonlinear Schr\u00f6dinger equation. J. Comput. Math. 4(2), 121\u2013130 (1986)","journal-title":"J. Comput. Math."},{"issue":"3","key":"1058_CR32","doi-asserted-by":"publisher","first-page":"033819","DOI":"10.1103\/PhysRevA.80.033819","volume":"80","author":"T Hansson","year":"2009","unstructured":"Hansson, T., Anderson, D., Lisak, M.: Propagation of partially coherent solitons in saturable logarithmic media: a comparative analysis. Phys. Rev. A 80(3), 033819 (2009)","journal-title":"Phys. Rev. A"},{"key":"1058_CR33","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/j.na.2018.03.017","volume":"173","author":"M Hayashi","year":"2018","unstructured":"Hayashi, M.: A note on the nonlinear Schr\u00f6dinger equation in a general domain. Nonlinear Anal. 173, 99\u2013122 (2018)","journal-title":"Nonlinear Anal."},{"key":"1058_CR34","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1103\/PhysRevA.32.1201","volume":"32","author":"EF Hefter","year":"1985","unstructured":"Hefter, E.F.: Application of the nonlinear Schr\u00f6dinger equation with a logarithmic inhomogeneous term to nuclear physics. Phys. Rev. A 32, 1201\u20131204 (1985)","journal-title":"Phys. Rev. A"},{"issue":"11","key":"1058_CR35","doi-asserted-by":"publisher","first-page":"2147","DOI":"10.1142\/S0218202517500415","volume":"27","author":"P Henning","year":"2017","unstructured":"Henning, P., Peterseim, D.: Crank\u2013Nicolson Galerkin approximations to nonlinear Schr\u00f6dinger equations with rough potentials. Math. Models Methods Appl. Sci. 27(11), 2147\u20132184 (2017)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"1058_CR36","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/0378-4371(81)90066-2","volume":"105","author":"ES Hernandez","year":"1980","unstructured":"Hernandez, E.S., Remaud, B.: General properties of Gausson-conserving descriptions of quantal damped motion. Physica A 105, 130\u2013146 (1980)","journal-title":"Physica A"},{"issue":"7","key":"1058_CR37","doi-asserted-by":"publisher","first-page":"3022","DOI":"10.1016\/j.jde.2011.01.028","volume":"250","author":"LI Ignat","year":"2011","unstructured":"Ignat, L.I.: A splitting method for the nonlinear Schr\u00f6dinger equation. J. Diff. Eq. 250(7), 3022\u20133046 (2011)","journal-title":"J. Diff. Eq."},{"issue":"6","key":"1058_CR38","doi-asserted-by":"publisher","first-page":"1779","DOI":"10.1137\/S0036142997330111","volume":"36","author":"O Karakashian","year":"1999","unstructured":"Karakashian, O., Makridakis, C.: A space-time finite element method for the nonlinear Schr\u00f6dinger equation: the continuous Galerkin method. SIAM J. Numer. Anal. 36(6), 1779\u20131807 (1999)","journal-title":"SIAM J. Numer. Anal."},{"key":"1058_CR39","doi-asserted-by":"publisher","first-page":"3122","DOI":"10.1103\/PhysRevE.61.3122","volume":"61","author":"W Krolikowski","year":"2000","unstructured":"Krolikowski, W., Edmundson, D., Bang, O.: Unified model for partially coherent solitons in logarithmically nonlinear media. Phys. Rev. E 61, 3122\u20133126 (2000)","journal-title":"Phys. Rev. E"},{"issue":"264","key":"1058_CR40","doi-asserted-by":"publisher","first-page":"2141","DOI":"10.1090\/S0025-5718-08-02101-7","volume":"77","author":"C Lubich","year":"2008","unstructured":"Lubich, C.: On splitting methods for Schr\u00f6dinger\u2013Poisson and cubic nonlinear Schr\u00f6dinger equations. Math. Comp. 77(264), 2141\u20132153 (2008)","journal-title":"Math. Comp."},{"issue":"4","key":"1058_CR41","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/s002110050406","volume":"81","author":"PA Markowich","year":"1999","unstructured":"Markowich, P.A., Pietra, P., Pohl, C.: Numerical approximation of quadratic observables of Schr\u00f6dinger-type equations in the semi-classical limit. Numer. Math. 81(4), 595\u2013630 (1999)","journal-title":"Numer. Math."},{"key":"1058_CR42","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1209\/epl\/i2003-00547-6","volume":"63","author":"SD Martino","year":"2003","unstructured":"Martino, S.D., Falanga, M., Godano, C., Lauro, G.: Logarithmic Schr\u00f6dinger-like equation as a model for magma transport. Europhys. Lett. 63, 472\u2013475 (2003)","journal-title":"Europhys. Lett."},{"key":"1058_CR43","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1017\/S0962492902000053","volume":"11","author":"RI McLachlan","year":"2002","unstructured":"McLachlan, R.I., Quispel, G.R.W.: Splitting methods. Acta Numerica 11, 341\u2013434 (2002)","journal-title":"Acta Numerica"},{"issue":"1","key":"1058_CR44","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1006\/jcph.1993.1029","volume":"104","author":"M Robinson","year":"1993","unstructured":"Robinson, M., Fairweather, G., Herbst, B.: On the numerical solution of the cubic Schr\u00f6dinger equation in one space variable. J. Comput. Phys. 104(1), 277\u2013284 (1993)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"1058_CR45","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1007\/s00526-014-0796-8","volume":"54","author":"M Squassina","year":"2015","unstructured":"Squassina, M., Szulkin, A.: Multiple solutions to logarithmic Schr\u00f6dinger equations with periodic potential. Calc. Var. Partial Differ. Eq. 54(1), 585\u2013597 (2015)","journal-title":"Calc. Var. Partial Differ. Eq."},{"issue":"2","key":"1058_CR46","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/0021-9991(84)90003-2","volume":"55","author":"TR Taha","year":"1984","unstructured":"Taha, T.R., Ablowitz, M.I.: Analytical and numerical aspects of certain nonlinear evolution equations II. Numerical, nonlinear Schr\u00f6dinger equation. J. Comput. Phys. 55(2), 203\u2013230 (1984)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1058_CR47","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/s00526-017-1122-z","volume":"56","author":"K Tanaka","year":"2017","unstructured":"Tanaka, K., Zhang, C.: Multi-bump solutions for logarithmic Schr\u00f6dinger equations. Calc. Var. Partial Differ. Eq. 56(2), 33 (2017)","journal-title":"Calc. Var. Partial Differ. Eq."},{"issue":"3","key":"1058_CR48","doi-asserted-by":"publisher","first-page":"822","DOI":"10.1016\/j.jcp.2008.10.008","volume":"228","author":"M Thalhammer","year":"2009","unstructured":"Thalhammer, M., Caliari, M., Neuhauser, C.: High-order time-splitting Hermite and Fourier spectral methods. J. Comput. Phys. 228(3), 822\u2013832 (2009)","journal-title":"J. Comput. Phys."},{"issue":"1\u20132","key":"1058_CR49","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1016\/0003-4916(78)90279-8","volume":"114","author":"K Yasue","year":"1978","unstructured":"Yasue, K.: Quantum mechanics of nonconservative systems. Ann. Phys. 114(1\u20132), 479\u2013496 (1978)","journal-title":"Ann. Phys."},{"key":"1058_CR50","first-page":"116","volume":"1","author":"Y Zhu","year":"1983","unstructured":"Zhu, Y.: Implicit difference schemes for the generalized non-linear Schr\u00f6dinger system. J. Comput. Math. 1, 116\u2013129 (1983)","journal-title":"J. Comput. Math."},{"key":"1058_CR51","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1134\/S0202289310040067","volume":"16","author":"KG Zloshchastiev","year":"2010","unstructured":"Zloshchastiev, K.G.: Logarithmic nonlinearity in theories of quantum gravity: origin of time and observational consequences. Grav. Cosmol. 16, 288\u2013297 (2010)","journal-title":"Grav. Cosmol."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-019-01058-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-019-01058-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-019-01058-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,13]],"date-time":"2020-07-13T23:07:25Z","timestamp":1594681645000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-019-01058-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,15]]},"references-count":51,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,10]]}},"alternative-id":["1058"],"URL":"https:\/\/doi.org\/10.1007\/s00211-019-01058-2","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,15]]},"assertion":[{"value":"2 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 May 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 July 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}