{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T07:15:00Z","timestamp":1783667700241,"version":"3.55.0"},"reference-count":46,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171385"],"award-info":[{"award-number":["12171385"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.cam.2026.117876","type":"journal-article","created":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T15:41:20Z","timestamp":1780674080000},"page":"117876","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["High order complex time integration with artificial compressibility bootstrapping for incompressible Navier-Stokes equations"],"prefix":"10.1016","volume":"489","author":[{"given":"Henghui","family":"Tang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaojing","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chunlong","family":"Hai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3468-8803","authenticated-orcid":false,"given":"Liquan","family":"Mei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"3-4","key":"10.1016\/j.cam.2026.117876_bib0001","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0045-7825(99)00193-0","article-title":"High-order accurate time-stepping schemes for convection-diffusion problems","volume":"182","author":"Donea","year":"2000","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"5","key":"10.1016\/j.cam.2026.117876_bib0002","doi-asserted-by":"crossref","first-page":"3123","DOI":"10.1137\/16M1061588","article-title":"Long time stability of high order multistep numerical schemes for two-dimensional incompressible Navier\u2013Stokes equations","volume":"54","author":"Cheng","year":"2016","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"10.1016\/j.cam.2026.117876_bib0003","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s10915-015-0015-6","article-title":"High order semi-Lagrangian methods for the incompressible Navier-Stokes equations","volume":"66","author":"Celledoni","year":"2015","journal-title":"J. Sci. Comput."},{"issue":"6","key":"10.1016\/j.cam.2026.117876_bib0004","doi-asserted-by":"crossref","first-page":"1967","DOI":"10.1002\/num.22852","article-title":"Higher order weak Galerkin methods for the Navier-Stokes equations with large Reynolds number","volume":"38","author":"Zhao","year":"2021","journal-title":"Numer. Methods Partial Differ. Eq."},{"issue":"3","key":"10.1016\/j.cam.2026.117876_bib0005","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s10543-009-0236-x","article-title":"High order splitting methods for analytic semigroups exist","volume":"49","author":"Hansen","year":"2009","journal-title":"BIT Numer. Math."},{"issue":"264","key":"10.1016\/j.cam.2026.117876_bib0006","doi-asserted-by":"crossref","first-page":"2097","DOI":"10.1090\/S0025-5718-08-02127-3","article-title":"The euler implicit\/explicit scheme for the 2D time-dependent Navier-Stokes equations with smooth or non-smooth initial data","volume":"77","author":"He","year":"2008","journal-title":"Math. Comput."},{"issue":"8","key":"10.1016\/j.cam.2026.117876_bib0007","doi-asserted-by":"crossref","first-page":"3041","DOI":"10.1016\/j.jcp.2011.11.028","article-title":"Accuracy analysis of explicit Runge-Kutta methods applied to the incompressible Navier-Stokes equations","volume":"231","author":"Sanderse","year":"2012","journal-title":"J. Comput. Phys."},{"issue":"5","key":"10.1016\/j.cam.2026.117876_bib0008","doi-asserted-by":"crossref","first-page":"A3366","DOI":"10.1137\/21M145793X","article-title":"Invariant-domain-preserving high-Order time stepping: i. explicit runge\u2013Kutta schemes","volume":"44","author":"Ern","year":"2022","journal-title":"SIAM J. Sci. Comput."},{"issue":"174","key":"10.1016\/j.cam.2026.117876_bib0009","first-page":"491","article-title":"Numerical solution of nonlinear differential equations with algebraic constraints. I. convergence results for backward differentiation formulas","volume":"46","author":"L\u00f6tstedt","year":"1986","journal-title":"Math. Comput."},{"key":"10.1016\/j.cam.2026.117876_bib0010","doi-asserted-by":"crossref","DOI":"10.1007\/s40304-024-00404-7","article-title":"Time-Implicit high-order accurate positivity-Preserving discretizations for the Navier-stokes and Navier-Stokes-Korteweg equations","author":"Meng","year":"2024","journal-title":"Commun. Math. Stat."},{"issue":"5","key":"10.1016\/j.cam.2026.117876_bib0011","doi-asserted-by":"crossref","first-page":"A2911","DOI":"10.1137\/18M1203808","article-title":"Constructing new time integrators using interpolating polynomials","volume":"41","author":"Buvoli","year":"2019","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"10.1016\/j.cam.2026.117876_bib0012","doi-asserted-by":"crossref","first-page":"1795","DOI":"10.1137\/130931035","article-title":"Numerical algorithms based on analytic function values at roots of unity","volume":"52","author":"Austin","year":"2014","journal-title":"SIAM J. Numer. Anal."},{"issue":"152","key":"10.1016\/j.cam.2026.117876_bib0013","first-page":"1181","article-title":"Integrating ODE\u2019s in the complex plane-Pole vaulting","volume":"35","author":"Corliss","year":"1980","journal-title":"Math. Comput."},{"issue":"2","key":"10.1016\/j.cam.2026.117876_bib0014","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1016\/j.jcp.2005.08.032","article-title":"Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods","volume":"213","author":"Tokman","year":"2006","journal-title":"J. Comput. Phys."},{"issue":"24","key":"10.1016\/j.cam.2026.117876_bib0015","doi-asserted-by":"crossref","first-page":"8762","DOI":"10.1016\/j.jcp.2011.08.023","article-title":"A new class of exponential propagation iterative methods of Runge-Kutta type (EPIRK)","volume":"230","author":"Tokman","year":"2011","journal-title":"J. Comput. Phys."},{"issue":"5","key":"10.1016\/j.cam.2026.117876_bib0016","doi-asserted-by":"crossref","first-page":"A2650","DOI":"10.1137\/110849961","article-title":"New adaptive exponential propagation iterative methods of runge\u2013Kutta type","volume":"34","author":"Tokman","year":"2012","journal-title":"SIAM J. Sci. Comput."},{"issue":"44-47","key":"10.1016\/j.cam.2026.117876_bib0017","doi-asserted-by":"crossref","first-page":"6011","DOI":"10.1016\/j.cma.2005.10.010","article-title":"An overview of projection methods for incompressible flows","volume":"195","author":"Guermond","year":"2006","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"2","key":"10.1016\/j.cam.2026.117876_bib0018","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1016\/j.jcp.2006.01.019","article-title":"A finite element penalty-projection method for incompressible flows","volume":"217","author":"Jobelin","year":"2006","journal-title":"J. Comput. Phys."},{"issue":"1","key":"10.1016\/j.cam.2026.117876_bib0019","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1137\/040604418","article-title":"Error analysis of pressure-Correction schemes for the time-Dependent stokes equations with open boundary conditions","volume":"43","author":"Guermond","year":"2005","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"10.1016\/j.cam.2026.117876_bib0020","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1006\/jcph.2001.6715","article-title":"Accurate projection methods for the incompressible Navier-stokes equations","volume":"168","author":"Brown","year":"2001","journal-title":"J. Comput. Phys."},{"issue":"1","key":"10.1016\/j.cam.2026.117876_bib0021","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/BF01061454","article-title":"Boundary conditions for incompressible flows","volume":"1","author":"Orszag","year":"1986","journal-title":"J. Sci. Comput."},{"issue":"4","key":"10.1016\/j.cam.2026.117876_bib0022","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.4208\/cicp.OA-2018-0016","article-title":"Vector penalty-Projection methods for open boundary conditions with optimal second-Order accuracy","volume":"26","author":"Angot","year":"2019","journal-title":"Commun. Comput. Phys."},{"issue":"313","key":"10.1016\/j.cam.2026.117876_bib0023","doi-asserted-by":"crossref","first-page":"2159","DOI":"10.1090\/mcom\/3309","article-title":"On the error estimates of the vector penalty-projection methods: second-order scheme","volume":"87","author":"Angot","year":"2017","journal-title":"Math. Comput."},{"issue":"248","key":"10.1016\/j.cam.2026.117876_bib0024","doi-asserted-by":"crossref","first-page":"1719","DOI":"10.1090\/S0025-5718-03-01621-1","article-title":"On the error estimates for the rotational pressure-correction projection methods","volume":"73","author":"Guermond","year":"2003","journal-title":"Math. Comput."},{"issue":"2","key":"10.1016\/j.cam.2026.117876_bib0025","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.cam.2008.08.014","article-title":"On the penalty-projection method for the Navier-stokes equations with the MAC mesh","volume":"226","author":"F\u00e9vri\u00e8re","year":"2009","journal-title":"J. Comput. Appl. Math."},{"issue":"4","key":"10.1016\/j.cam.2026.117876_bib0026","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1051\/m2an\/2017016","article-title":"Convergence of a vector penalty projection scheme for the Navier-Stokes equations with moving body","volume":"52","author":"Bruneau","year":"2018","journal-title":"ESAIM: Math. Model. Numer. Anal."},{"key":"10.1016\/j.cam.2026.117876_bib0027","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1016\/j.cma.2017.07.033","article-title":"A conservative, second order, unconditionally stable artificial compression method","volume":"325","author":"DeCaria","year":"2017","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"1","key":"10.1016\/j.cam.2026.117876_bib0028","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0168-9274(95)00132-8","article-title":"On a new pseudocompressibility method for the incompressible Navier-Stokes equations","volume":"21","author":"Shen","year":"1996","journal-title":"Appl. Numer. Math."},{"issue":"3","key":"10.1016\/j.cam.2026.117876_bib0029","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1002\/num.22331","article-title":"An analysis of the robert-asselin time filter for the correction of nonphysical acoustics in an artificial compression method","volume":"35","author":"DeCaria","year":"2018","journal-title":"Numer. Methods Partial Differ. Equ."},{"issue":"3","key":"10.1016\/j.cam.2026.117876_bib0030","doi-asserted-by":"crossref","first-page":"1458","DOI":"10.1007\/s10915-018-0670-5","article-title":"Numerical analysis of an artificial compression method for magnetohydrodynamic flows at low magnetic reynolds numbers","volume":"76","author":"Rong","year":"2018","journal-title":"J. Sci. Comput."},{"issue":"2","key":"10.1016\/j.cam.2026.117876_bib0031","doi-asserted-by":"crossref","first-page":"A770","DOI":"10.1137\/18M1209301","article-title":"High-Order adaptive time stepping for the incompressible Navier\u2013Stokes equations","volume":"41","author":"Guermond","year":"2019","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"10.1016\/j.cam.2026.117876_bib0032","doi-asserted-by":"crossref","first-page":"A2656","DOI":"10.1137\/140975231","article-title":"High-Order time stepping for the incompressible Navier\u2013Stokes equations","volume":"37","author":"Guermond","year":"2015","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"10.1016\/j.cam.2026.117876_bib0033","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1515\/jnma-2019-0015","article-title":"Doubly-adaptive artificial compression methods for incompressible flow","volume":"28","author":"Layton","year":"2020","journal-title":"J. Numer. Math."},{"issue":"3","key":"10.1016\/j.cam.2026.117876_bib0034","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1137\/130932132","article-title":"The exponentially convergent trapezoidal rule","volume":"56","author":"Trefethen","year":"2014","journal-title":"SIAM Rev."},{"issue":"1","key":"10.1016\/j.cam.2026.117876_bib0035","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10208-010-9075-z","article-title":"Accuracy and stability of computing high-order derivatives of analytic functions by cauchy integrals","volume":"11","author":"Bornemann","year":"2010","journal-title":"Found. Comput. Math."},{"issue":"19","key":"10.1016\/j.cam.2026.117876_bib0036","doi-asserted-by":"crossref","first-page":"7013","DOI":"10.1016\/j.jcp.2010.05.037","article-title":"An unconditionally stable rotational velocity-correction scheme for incompressible flows","volume":"229","author":"Dong","year":"2010","journal-title":"J. Comput. Phys."},{"issue":"19","key":"10.1016\/j.cam.2026.117876_bib0037","doi-asserted-by":"crossref","first-page":"7250","DOI":"10.1016\/j.jcp.2009.06.021","article-title":"Open and traction boundary conditions for the incompressible Navier-Stokes equations","volume":"228","author":"Liu","year":"2009","journal-title":"J. Comput. Phys."},{"issue":"1","key":"10.1016\/j.cam.2026.117876_bib0038","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.jcp.2004.02.009","article-title":"Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term","volume":"199","author":"Johnston","year":"2004","journal-title":"J. Comput. Phys."},{"issue":"2","key":"10.1016\/j.cam.2026.117876_bib0039","doi-asserted-by":"crossref","DOI":"10.1007\/s10543-026-01120-0","article-title":"On the conjecture of stability preservation in arbitrary-Order adams-Bashforth-Type integrators","volume":"66","author":"Yin","year":"2026","journal-title":"BIT Numer. Math."},{"key":"10.1016\/j.cam.2026.117876_bib0040","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2026.118791","article-title":"Energy-stable decoupled numerical approximation with practical correction technique for the binary phase field darcy fluid system","volume":"452","author":"Ren","year":"2026","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.cam.2026.117876_bib0041","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2025.109381","article-title":"Phase-field modeling and numerical computation for the hydrodynamics coupled diblock copolymer in complex geometries","volume":"152","author":"Zhang","year":"2026","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"10.1016\/j.cam.2026.117876_bib0042","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2025.114561","article-title":"A diffuse interface model and fully decoupled, energy-stable scheme for the two-phase ferrofluid flows in porous media","volume":"548","author":"Zhang","year":"2026","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.cam.2026.117876_bib0043","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2022.111026","article-title":"A second-order time accurate and fully-decoupled numerical scheme of the darcy-Newtonian-Nematic model for two-phase complex fluids confined in the hele-Shaw cell","volume":"456","author":"Chen","year":"2022","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.cam.2026.117876_bib0044","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2021.110342","article-title":"Efficient and energy stable scheme for the hydrodynamically coupled three components cahn-Hilliard phase-field model using the stabilized-invariant energy quadratization (S-IEQ) approach","volume":"438","author":"Yang","year":"2021","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.cam.2026.117876_bib0045","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2024.113365","article-title":"Efficient energy stable schemes for incompressible flows with variable density","volume":"517","author":"Li","year":"2024","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.cam.2026.117876_bib0046","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2025.109303","article-title":"Consistently energy-stable decoupled method with second-order accuracy and lower density bounds for the incompressible fluid flows with variable density","volume":"152","author":"Zhang","year":"2026","journal-title":"Commun. Nonlinear Sci. Numer. Simul."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005182?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005182?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T06:44:15Z","timestamp":1783665855000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726005182"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":46,"alternative-id":["S0377042726005182"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117876","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"High order complex time integration with artificial compressibility bootstrapping for incompressible Navier-Stokes equations","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117876","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117876"}}