{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T06:26:23Z","timestamp":1781504783393,"version":"3.54.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T00:00:00Z","timestamp":1723507200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T00:00:00Z","timestamp":1723507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"National Key Research and Development Program of China","award":["2021YFA1003004"],"award-info":[{"award-number":["2021YFA1003004"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12272347"],"award-info":[{"award-number":["12272347"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1007\/s10915-024-02647-6","type":"journal-article","created":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T05:02:01Z","timestamp":1723525321000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Local Discontinuous Galerkin Methods with Multistep Implicit\u2013Explicit Time Discretization for Nonlinear Schr\u00f6dinger Equations"],"prefix":"10.1007","volume":"101","author":[{"given":"Ying","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3681-9598","authenticated-orcid":false,"given":"Xinghui","family":"Zhong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,8,13]]},"reference":[{"key":"2647_CR1","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719208","volume-title":"The Finite Element Method for Elliptic Problems","author":"PG Ciarlet","year":"2002","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2002)"},{"issue":"1","key":"2647_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10915-019-01102-1","volume":"82","author":"A Chen","year":"2020","unstructured":"Chen, A., Cheng, Y., Liu, Y., Zhang, M.: Superconvergence of ultra-weak discontinuous Galerkin methods for the linear Sch\u00f6dinger equation in one dimension. J. Sci. Comput. 82(1), 1\u201344 (2020)","journal-title":"J. Sci. Comput."},{"issue":"238","key":"2647_CR3","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1090\/S0025-5718-01-01317-5","volume":"71","author":"P Castillo","year":"2002","unstructured":"Castillo, P., Cockburn, B., Sch\u00f6tzau, D., Schwab, C.: Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for the convection-diffusion problems. Math. Comput. 71(238), 455\u2013478 (2002)","journal-title":"Math. Comput."},{"issue":"3","key":"2647_CR4","doi-asserted-by":"crossref","first-page":"1444","DOI":"10.1007\/s10915-018-0708-8","volume":"77","author":"P Castillo","year":"2018","unstructured":"Castillo, P., G\u00f3mez, S.: On the conservation of fractional nonlinear Schr\u00f6dinger equation\u2019s invariants by the local discontinuous Galerkin method. J. Sci. Comput. 77(3), 1444\u20131467 (2018)","journal-title":"J. Sci. Comput."},{"issue":"190","key":"2647_CR5","first-page":"545","volume":"54","author":"B Cockburn","year":"1990","unstructured":"Cockburn, B., Hou, S., Shu, C..-W.: The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case. Math. Comput. 54(190), 545\u2013581 (1990)","journal-title":"Math. Comput."},{"issue":"2","key":"2647_CR6","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1007\/s10915-018-0789-4","volume":"78","author":"A Chen","year":"2019","unstructured":"Chen, A., Li, F., Cheng, Y.: An ultra-weak discontinuous Galerkin method for Schr\u00f6dinger equation in one dimension. J. Sci. Comput. 78(2), 772\u2013815 (2019)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"2647_CR7","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/0021-9991(89)90183-6","volume":"84","author":"B Cockburn","year":"1989","unstructured":"Cockburn, B., Lin, S..Y., Shu, C..-W..: TVB Runge\u2013Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems. J. Comput. Phys. 84(1), 90\u2013113 (1989)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"2647_CR8","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1023\/A:1012873910884","volume":"16","author":"B Cockburn","year":"2001","unstructured":"Cockburn, B., Shu, C.-W.: Runge\u2013Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16(3), 173\u2013261 (2001)","journal-title":"J. Sci. Comput."},{"issue":"6","key":"2647_CR9","doi-asserted-by":"crossref","first-page":"2440","DOI":"10.1137\/S0036142997316712","volume":"35","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.-W.: The local discontinuous Galerkin method for time-dependent convection\u2013diffusion systems. SIAM J. Numer. Anal. 35(6), 2440\u20132463 (1998)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"2647_CR10","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1006\/jcph.1998.5892","volume":"141","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C..-W.: The Runge\u2013Kutta discontinuous Galerkin method for conservation laws. V: multidimensional systems. J. Comput. Phys. 141(2), 199\u2013224 (1998)","journal-title":"J. Comput. Phys."},{"key":"2647_CR11","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1051\/m2an\/1991250303371","volume":"25","author":"B Cockburn","year":"1991","unstructured":"Cockburn, B., Shu, C.-W.: The Runge\u2013Kutta local projection $$P^1$$-discontinuous Galerkin method for scalar conservation laws. Math. Model. Numer. Anal. 25, 337\u2013361 (1991)","journal-title":"Math. Model. Numer. Anal."},{"issue":"186","key":"2647_CR12","first-page":"411","volume":"52","author":"B Cockburn","year":"1989","unstructured":"Cockburn, B., Shu, C..-W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II: General framework. Math. Comput. 52(186), 411\u2013435 (1989)","journal-title":"Math. Comput."},{"issue":"1\u20132","key":"2647_CR13","first-page":"247","volume":"174","author":"I Da\u01e7","year":"1999","unstructured":"Da\u01e7, I.: A quadratic B-spline finite element method for solving nonlinear Schr\u00f6dinger equation. Comput. Methods Appl. Mech. Eng. 174(1\u20132), 247\u2013258 (1999)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"2647_CR14","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s10915-015-0022-7","volume":"66","author":"B Dong","year":"2016","unstructured":"Dong, B., Shu, C.-W., Wang, W.: A new multiscale discontinuous Galerkin method for the one-dimensional stationary Schr\u00f6dinger equation. J. Sci. Comput. 66(1), 321\u2013345 (2016)","journal-title":"J. Sci. Comput."},{"key":"2647_CR15","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.apnum.2016.06.003","volume":"109","author":"Y Gao","year":"2016","unstructured":"Gao, Y., Mei, L.: Implicit-explicit multistep methods for general two-dimensional nonlinear Schr\u00f6dinger equations. Appl. Numer. Math. 109, 41\u201360 (2016)","journal-title":"Appl. Numer. Math."},{"key":"2647_CR16","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/j.jcp.2016.10.022","volume":"328","author":"Y Gong","year":"2017","unstructured":"Gong, Y., Wang, Q., Wang, Y., Cai, J.: A conservative Fourier pseudo-spectral method for the nonlinear Schr\u00f6dinger equation. J. Comput. Phys. 328, 354\u2013370 (2017)","journal-title":"J. Comput. Phys."},{"key":"2647_CR17","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1007\/s10915-014-9977-z","volume":"65","author":"L Guo","year":"2015","unstructured":"Guo, L., Xu, Y.: Energy conserving local discontinuous Galerkin methods for the nonlinear Schr\u00f6dinger equation with wave operator. J. Sci. Comput. 65, 622\u2013647 (2015)","journal-title":"J. Sci. Comput."},{"key":"2647_CR18","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.apnum.2018.01.004","volume":"127","author":"J Hong","year":"2018","unstructured":"Hong, J., Ji, L., Liu, Z.: Optimal error estimate of conservative local discontinuous Galerkin method for nonlinear Schr\u00f6dinger equation. Applied Numerical Mathematics: Transactions of IMACS 127, 164\u2013178 (2018)","journal-title":"Applied Numerical Mathematics: Transactions of IMACS"},{"key":"2647_CR19","first-page":"100","volume":"343","author":"B Ji","year":"2019","unstructured":"Ji, B., Zhang, L.: Error estimate of exponential wave integrator Fourier pseudospectral methods for the nonlinear Schr\u00f6dinger equation. Appl. Math. Comput. 343, 100\u2013113 (2019)","journal-title":"Appl. Math. Comput."},{"issue":"6","key":"2647_CR20","doi-asserted-by":"crossref","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":"2647_CR21","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.jcp.2017.12.044","volume":"358","author":"M Li","year":"2018","unstructured":"Li, M., Gu, X.M., Huang, C., Fei, M., Zhang, G.: A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schr\u00f6dinger equations. J. Comput. Phys. 358, 256\u2013282 (2018)","journal-title":"J. Comput. Phys."},{"key":"2647_CR22","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.jcp.2014.11.014","volume":"282","author":"W Lu","year":"2015","unstructured":"Lu, W., Huang, Y., Liu, H.: Mass preserving discontinuous Galerkin methods for Schr\u00f6dinger equations. J. Comput. Phys. 282, 210\u2013226 (2015)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2647_CR23","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1093\/imanum\/dry012","volume":"39","author":"H Liu","year":"2019","unstructured":"Liu, H., Huang, Y., Lu, W., Yi, N.: On accuracy of the mass-preserving DG method to multi-dimensional Schr\u00f6dinger equations. IMA J. Numer. Anal. 39(2), 760\u2013791 (2019)","journal-title":"IMA J. Numer. Anal."},{"key":"2647_CR24","first-page":"1","volume":"S4","author":"P Lasaint","year":"1974","unstructured":"Lasaint, P., Raviart, P.A.: On a finite element method for solving the neutron transport equation. Publications math\u00e9matiques et informatique de Rennes S4, 1\u201340 (1974)","journal-title":"Publications math\u00e9matiques et informatique de Rennes"},{"key":"2647_CR25","unstructured":"Reed, W.H. , Hill,T.: Triangular mesh methods for the neutron transport equation, Los Alamos Scientific Lab., N. Mex.(USA). (1973)"},{"issue":"5","key":"2647_CR26","doi-asserted-by":"crossref","first-page":"2336","DOI":"10.1137\/16M1094324","volume":"55","author":"RR Rosales","year":"2017","unstructured":"Rosales, R.R., Seibold, B., Shirokoff, D., Zhou, D.: Unconditional stability for multistep IMEX schemes-theory. SIAM J. Numer. Anal. 55(5), 2336\u20132360 (2017)","journal-title":"SIAM J. Numer. Anal."},{"key":"2647_CR27","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1016\/j.cam.2015.07.030","volume":"292","author":"H Song","year":"2016","unstructured":"Song, H.: Energy SSP-IMEX Runge-Kutta methods for the Cahn-Hilliard equation. J. Comput. Appl. Math. 292, 576\u2013590 (2016)","journal-title":"J. Comput. Appl. Math."},{"key":"2647_CR28","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.jcp.2018.09.044","volume":"376","author":"B Seibold","year":"2019","unstructured":"Seibold, B., Shirokoff, D., Zhou, D.: Unconditional stability for multistep IMEX schemes-practice. J. Comput. Phys. 376, 295\u2013321 (2019)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"2647_CR29","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1007\/s10915-017-0390-2","volume":"72","author":"D Shi","year":"2017","unstructured":"Shi, D., Wang, J.: Unconditional superconvergence analysis of a Crank-Nicolson Galerkin FEM for nonlimear Schr\u00f6dinger equation. J. Sci. Comput. 72(3), 1093\u20131118 (2017)","journal-title":"J. Sci. Comput."},{"key":"2647_CR30","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.cam.2019.01.033","volume":"356","author":"Q Tao","year":"2019","unstructured":"Tao, Q., Xia, Y.: Error estimates and post-processing of local discontinuous Galerkin method for Schr\u00f6dinger equations. J. Comput. Appl. Math. 356, 198\u2013218 (2019)","journal-title":"J. Comput. Appl. Math."},{"key":"2647_CR31","first-page":"31","volume":"01","author":"J Wang","year":"2007","unstructured":"Wang, J.: Multisymplectic Fourier pseudospectral method for the nonlinear Schr\u00f6dinger equations with wave operator. J. Comput. Math. 01, 31\u201348 (2007)","journal-title":"J. Comput. Math."},{"issue":"315","key":"2647_CR32","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1090\/mcom\/3312","volume":"88","author":"H Wang","year":"2019","unstructured":"Wang, H., Liu, Y., Zhang, Q., Shu, C.-W.: Local discontinuous Galerkin methods with implicit-explicit time-marching for time-dependent incompressible fluid flow. Math. Comput. 88(315), 91\u2013121 (2019)","journal-title":"Math. Comput."},{"key":"2647_CR33","first-page":"237","volume":"272","author":"H Wang","year":"2016","unstructured":"Wang, H., Shu, C.-W., Zhang, Q.: Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems. Appl. Math. Comput. 272, 237\u2013258 (2016)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"2647_CR34","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1137\/140956750","volume":"53","author":"H Wang","year":"2015","unstructured":"Wang, H., Shu, C.-W., Zhang, Q.: Stability and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for advection-diffusion problems. SIAM J. Numer. Anal. 53(1), 206\u2013227 (2015)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"2647_CR35","doi-asserted-by":"crossref","first-page":"1931","DOI":"10.1051\/m2an\/2017017","volume":"51","author":"H Wang","year":"2017","unstructured":"Wang, H., Zhang, Q., Shu, C..-W.: Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs. ESAIM: Mathematical Modelling and Numerical Analysis 51(5), 1931\u20131955 (2017)","journal-title":"ESAIM: Mathematical Modelling and Numerical Analysis"},{"key":"2647_CR36","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.cam.2018.04.004","volume":"342","author":"H Wang","year":"2018","unstructured":"Wang, H., Zhang, Q., Shu, C.-W.: Third order implicit-explicit Runge-Kutta local discontinuous Galerkin methods with suitable boundary treatment for convection-diffusion problems with Dirichlet boundary conditions. J. Comput. Appl. Math. 342, 164\u2013179 (2018)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"2647_CR37","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s11425-018-9524-x","volume":"63","author":"H Wang","year":"2020","unstructured":"Wang, H., Zhang, Q., Wang, S., Shu, C.-W.: Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems. SCIENCE CHINA Math. 63(1), 183\u2013204 (2020)","journal-title":"SCIENCE CHINA Math."},{"issue":"4","key":"2647_CR38","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1051\/m2an\/2015068","volume":"50","author":"H Wang","year":"2016","unstructured":"Wang, H., Wang, S., Zhang, Q., Shu, C..-W.: Local discontinuous Galerkin methods with implicit-explicit time-marching for multi-dimensional convection-diffusion problems. ESAIM: Mathematical Modelling and Numerical Analysis 50(4), 1083\u20131105 (2016)","journal-title":"ESAIM: Mathematical Modelling and Numerical Analysis"},{"issue":"1","key":"2647_CR39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10915-018-0752-4","volume":"78","author":"H Wang","year":"2019","unstructured":"Wang, H., Zheng, J., Yu, F., Guo, H., Zhang, Q.: Local discontinuous Galerkin method with implicit-explicit time marching for incompressible miscible displacement problem in porous media. J. Sci. Comput. 78(1), 1\u201328 (2019)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"2647_CR40","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.jcp.2004.11.001","volume":"205","author":"Y Xu","year":"2005","unstructured":"Xu, Y., Shu, C.-W.: Local discontinuous Galerkin methods for nonlinear Schr\u00f6dinger equations. J. Comput. Phys. 205(1), 72\u201397 (2005)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2647_CR41","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1137\/11082258X","volume":"50","author":"Y Xu","year":"2012","unstructured":"Xu, Y., Shu, C.-W.: Optimal error estimates of the semidiscrete local discontinuous Galerkin methods for high order wave equations. SIAM J. Numer. Anal. 50(1), 79\u2013104 (2012)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"2647_CR42","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s10915-011-9498-y","volume":"51","author":"Q Zhang","year":"2012","unstructured":"Zhang, Q., Gao, F.: A fully-discrete local discontinuous Galerkin method for convection-dominated Sobolev equation. J. Sci. Comput. 51(1), 107\u2013134 (2012)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"2647_CR43","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1137\/S0036142902404182","volume":"42","author":"Q Zhang","year":"2004","unstructured":"Zhang, Q., Shu, C.-W.: Error estimates to smooth solutions of Runge-Kutta discontinuous Galerkin methods for scalar conservation laws. SIAM J. Numer. Anal. 42(2), 641\u2013666 (2004)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"2647_CR44","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1137\/090771363","volume":"48","author":"Q Zhang","year":"2010","unstructured":"Zhang, Q., Shu, C.-W.: Stability analysis and a priori error estimates of the third order explicit Runge-Kutta discontinuous Galerkin method for scalar conservation laws. SIAM J. Numer. Anal. 48(3), 1038\u20131063 (2010)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"2647_CR45","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/s42967-020-00100-7","volume":"4","author":"H Zhang","year":"2022","unstructured":"Zhang, H., Wu, B., Meng, X.: A local discontinuous Galerkin method with generalized alternating fluxes for 2D nonlinear Schr\u00f6dinger equations. Communications on Applied Mathematics and Computation 4(1), 84\u2013107 (2022)","journal-title":"Communications on Applied Mathematics and Computation"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02647-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-024-02647-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-024-02647-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T10:09:39Z","timestamp":1726826979000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-024-02647-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,13]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["2647"],"URL":"https:\/\/doi.org\/10.1007\/s10915-024-02647-6","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,13]]},"assertion":[{"value":"27 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 June 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 July 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 August 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"4"}}