{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:21:22Z","timestamp":1757618482800,"version":"3.44.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T00:00:00Z","timestamp":1751328000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T00:00:00Z","timestamp":1751328000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["2309655"],"award-info":[{"award-number":["2309655"]}],"id":[{"id":"10.13039\/100000121","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":[[2025,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>In this paper, we study the uniform accuracy of implicit-explicit (IMEX) Runge-Kutta (RK) schemes for general linear hyperbolic relaxation systems satisfying the structural stability condition proposed in [34]. We establish the uniform stability and accuracy of a class of IMEX-RK schemes with spatial discretization using a Fourier spectral method. Our results demonstrate that the accuracy of the fully discretized schemes is independent of the relaxation time across all regimes. Numerical experiments on applications in traffic flows and kinetic theory verify our theoretical analysis.<\/jats:p>","DOI":"10.1007\/s10915-025-02972-4","type":"journal-article","created":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T07:57:31Z","timestamp":1751356651000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Uniform Accuracy of Implicit-Explicit Runge-Kutta Methods for Linear Hyperbolic Relaxation Systems"],"prefix":"10.1007","volume":"104","author":[{"given":"Zhiting","family":"Ma","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0527-7431","authenticated-orcid":false,"given":"Juntao","family":"Huang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,1]]},"reference":[{"issue":"4","key":"2972_CR1","doi-asserted-by":"publisher","first-page":"A2402","DOI":"10.1137\/19M1303290","volume":"42","author":"G Albi","year":"2020","unstructured":"Albi, G., Dimarco, G., Pareschi, L.: Implicit-explicit multistep methods for hyperbolic systems with multiscale relaxation. SIAM J. Sci. Comput. 42(4), A2402\u2013A2435 (2020)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2\u20133","key":"2972_CR2","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/S0168-9274(97)00056-1","volume":"25","author":"UM Ascher","year":"1997","unstructured":"Ascher, U.M., Ruuth, S.J., Spiteri, R.J.: Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25(2\u20133), 151\u2013167 (1997)","journal-title":"Appl. Numer. Math."},{"issue":"3","key":"2972_CR3","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1137\/0732037","volume":"32","author":"UM Ascher","year":"1995","unstructured":"Ascher, U.M., Ruuth, S.J., Wetton, B.T.R.: Implicit-explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal. 32(3), 797\u2013823 (1995)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"2972_CR4","doi-asserted-by":"publisher","first-page":"916","DOI":"10.1137\/S0036139997332099","volume":"60","author":"A Aw","year":"2000","unstructured":"Aw, A., Rascle, M.: Resurrection of \u201csecond order\u2019\u2019 models of traffic flow. SIAM J. Appl. Math. 60(3), 916\u2013938 (2000)","journal-title":"SIAM J. Appl. Math."},{"key":"2972_CR5","doi-asserted-by":"crossref","unstructured":"Bhatnagar, P., Gross, E., Krook, M.: A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems. Physical Review, 94(3):511\u2013525, (1954)","DOI":"10.1103\/PhysRev.94.511"},{"issue":"4","key":"2972_CR6","doi-asserted-by":"publisher","first-page":"1600","DOI":"10.1137\/060656929","volume":"45","author":"S Boscarino","year":"2007","unstructured":"Boscarino, S.: Error analysis of IMEX Runge-Kutta methods derived from differential-algebraic systems. SIAM J. Numer. Anal. 45(4), 1600\u20131621 (2007)","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"2972_CR7","doi-asserted-by":"publisher","first-page":"1926","DOI":"10.1137\/080713562","volume":"31","author":"S Boscarino","year":"2009","unstructured":"Boscarino, S., Russo, G.: On a class of uniformly accurate IMEX Runge-Kutta schemes and applications to hyperbolic systems with relaxation. SIAM J. Sci. Comput. 31(3), 1926\u20131945 (2009)","journal-title":"SIAM J. Sci. Comput."},{"issue":"8","key":"2972_CR8","doi-asserted-by":"publisher","first-page":"1243","DOI":"10.1063\/1.1711368","volume":"7","author":"JE Broadwell","year":"1964","unstructured":"Broadwell, J.E.: Shock structure in a simple discrete velocity gas. The Physics of Fluids 7(8), 1243\u20131247 (1964)","journal-title":"The Physics of Fluids"},{"issue":"3","key":"2972_CR9","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1002\/cpa.21472","volume":"67","author":"Z Cai","year":"2014","unstructured":"Cai, Z., Fan, Y., Li, R.: Globally hyperbolic regularization of grad\u2019s moment system. Communications on Pure and Applied Mathematics 67(3), 464\u2013518 (2014)","journal-title":"Communications on Pure and Applied Mathematics"},{"issue":"2","key":"2972_CR10","first-page":"255","volume":"10","author":"Y Di","year":"2017","unstructured":"Di, Y., Fan, Y., Li, R., Zheng, L.: Linear stability of hyperbolic moment models for boltzmann equation. Numerical Mathematics: Theory, Methods and Applications 10(2), 255\u2013277 (2017)","journal-title":"Numerical Mathematics: Theory, Methods and Applications"},{"issue":"2","key":"2972_CR11","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1137\/12087606X","volume":"51","author":"G Dimarco","year":"2013","unstructured":"Dimarco, G., Pareschi, L.: Asymptotic preserving implicit-explicit Runge-Kutta methods for nonlinear kinetic equations. SIAM J. Numer. Anal. 51(2), 1064\u20131087 (2013)","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"2972_CR12","doi-asserted-by":"publisher","first-page":"664","DOI":"10.1137\/16M1063824","volume":"55","author":"G Dimarco","year":"2017","unstructured":"Dimarco, G., Pareschi, L.: Implicit-explicit linear multistep methods for stiff kinetic equations. SIAM J. Numer. Anal. 55(2), 664\u2013690 (2017)","journal-title":"SIAM J. Numer. Anal."},{"key":"2972_CR13","doi-asserted-by":"crossref","unstructured":"Geroch, R., Lindblom, L.: Dissipative relativistic fluid theories of divergence type. Phys. Rev. D (3), 41(6):1855\u20131861, (1990)","DOI":"10.1103\/PhysRevD.41.1855"},{"key":"2972_CR14","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1007\/s11425-011-4346-y","volume":"55","author":"V Giovangigli","year":"2012","unstructured":"Giovangigli, V.: Multicomponent flow modeling. Science China Mathematics 55, 285\u2013308 (2012)","journal-title":"Science China Mathematics"},{"issue":"4","key":"2972_CR15","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1002\/cpa.3160020403","volume":"2","author":"H Grad","year":"1949","unstructured":"Grad, H.: On the kinetic theory of rarefied gases. Communications on pure and applied mathematics 2(4), 331\u2013407 (1949)","journal-title":"Communications on pure and applied mathematics"},{"key":"2972_CR16","unstructured":"Graham, A.: Kronecker products and matrix calculus: with applications. Ellis Horwood Series in Mathematics and its Applications. Ellis Horwood Ltd., Chichester; Halsted Press [John Wiley & Sons, Inc.], New York, (1981)"},{"issue":"3","key":"2972_CR17","first-page":"193","volume":"330","author":"B Hanouzet","year":"2000","unstructured":"Hanouzet, B., Huynh, P.: Approximation par relaxation d\u2019un syst\u00e8me de maxwell non lin\u00e9aire. Comptes Rendus de l\u2019Acad\u00e9mie des Sciences-Series I-Mathematics 330(3), 193\u2013198 (2000)","journal-title":"Comptes Rendus de l\u2019Acad\u00e9mie des Sciences-Series I-Mathematics"},{"key":"2972_CR18","doi-asserted-by":"crossref","unstructured":"Hesthaven, J.S., Gottlieb, S., Gottlieb, D.: Spectral methods for time-dependent problems. Cambridge Monographs on Applied and Computational Mathematics, vol. 21. Cambridge University Press, Cambridge (2007)","DOI":"10.1017\/CBO9780511618352"},{"key":"2972_CR19","doi-asserted-by":"crossref","unstructured":"Hu, J., Jin, S., Li, Q.: Asymptotic-preserving schemes for multiscale hyperbolic and kinetic equations. In Handbook of Numerical Analysis, volume\u00a018, pages 103\u2013129. Elsevier, (2017)","DOI":"10.1016\/bs.hna.2016.09.001"},{"issue":"328","key":"2972_CR20","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1090\/mcom\/3602","volume":"90","author":"J Hu","year":"2021","unstructured":"Hu, J., Shu, R.: On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations. Mathematics of Computation 90(328), 641\u2013670 (2021)","journal-title":"Mathematics of Computation"},{"key":"2972_CR21","doi-asserted-by":"crossref","unstructured":"Hu, J., Shu, R.: Uniform accuracy of implicit-explicit runge-kutta (IMEX-RK) schemes for hyperbolic systems with relaxation. arXiv preprint arXiv:2306.08742, (2023)","DOI":"10.1090\/mcom\/3967"},{"issue":"2","key":"2972_CR22","doi-asserted-by":"publisher","first-page":"2016","DOI":"10.1016\/j.jcp.2007.03.003","volume":"225","author":"W Hundsdorfer","year":"2007","unstructured":"Hundsdorfer, W., Ruuth, S.J.: IMEX extensions of linear multistep methods with general monotonicity and boundedness properties. J. Comput. Phys. 225(2), 2016\u20132042 (2007)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2972_CR23","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1137\/S1064827598334599","volume":"21","author":"S Jin","year":"1999","unstructured":"Jin, S.: Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations. SIAM J. Sci. Comput. 21(2), 441\u2013454 (1999)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"2972_CR24","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1002\/cpa.3160480303","volume":"48","author":"S Jin","year":"1995","unstructured":"Jin, S., Xin, Z.P.: The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Comm. Pure Appl. Math. 48(3), 235\u2013276 (1995)","journal-title":"Comm. Pure Appl. Math."},{"issue":"1\u20132","key":"2972_CR25","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/S0168-9274(02)00138-1","volume":"44","author":"CA Kennedy","year":"2003","unstructured":"Kennedy, C.A., Carpenter, M.H.: Additive runge-kutta schemes for convection-diffusion-reaction equations. Applied numerical mathematics 44(1\u20132), 139\u2013181 (2003)","journal-title":"Applied numerical mathematics"},{"key":"2972_CR26","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1007\/BF02179552","volume":"83","author":"CD Levermore","year":"1996","unstructured":"Levermore, C.D.: Moment closure hierarchies for kinetic theories. Journal of statistical Physics 83, 1021\u20131065 (1996)","journal-title":"Journal of statistical Physics"},{"key":"2972_CR27","unstructured":"Ma, Z., Huang, J., Yong, W.-A.: Uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for linear hyperbolic relaxation systems. arXiv preprint arXiv:2310.05342, (2023)"},{"issue":"13","key":"2972_CR28","doi-asserted-by":"publisher","first-page":"13741","DOI":"10.1002\/mma.9288","volume":"46","author":"Z Ma","year":"2023","unstructured":"Ma, Z., Yong, W.-A.: Nonrelativistic limit of the euler-hmpn approximation models arising in radiation hydrodynamics. Mathematical Methods in the Applied Sciences 46(13), 13741\u201313780 (2023)","journal-title":"Mathematical Methods in the Applied Sciences"},{"key":"2972_CR29","unstructured":"Mihalas, D., Mihalas, B.\u00a0W.: Foundations of radiation hydrodynamics. Courier Corporation, (2013)"},{"issue":"1\u20132","key":"2972_CR30","first-page":"129","volume":"25","author":"L Pareschi","year":"2005","unstructured":"Pareschi, L., Russo, G.: Implicit-Explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput. 25(1\u20132), 129\u2013155 (2005)","journal-title":"J. Sci. Comput."},{"issue":"2","key":"2972_CR31","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1137\/1030045","volume":"30","author":"T Platkowski","year":"1988","unstructured":"Platkowski, T., Illner, R.: Discrete velocity models of the boltzmann equation: a survey on the mathematical aspects of the theory. SIAM review 30(2), 213\u2013255 (1988)","journal-title":"SIAM review"},{"key":"2972_CR32","unstructured":"Pomraning, G.\u00a0C.: The equations of radiation hydrodynamics. Courier Corporation, (2005)"},{"issue":"125","key":"2972_CR33","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1090\/S0025-5718-1974-0331793-2","volume":"28","author":"A Prothero","year":"1974","unstructured":"Prothero, A., Robinson, A.: On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations. Mathematics of Computation 28(125), 145\u2013162 (1974)","journal-title":"Mathematics of Computation"},{"issue":"1","key":"2972_CR34","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1006\/jdeq.1998.3584","volume":"155","author":"W-A Yong","year":"1999","unstructured":"Yong, W.-A.: Singular perturbations of first-order hyperbolic systems with stiff source terms. Journal of Differential Equations 155(1), 89\u2013132 (1999)","journal-title":"Journal of Differential Equations"},{"key":"2972_CR35","doi-asserted-by":"crossref","unstructured":"Yong, W.-A.: Basic aspects of hyperbolic relaxation systems. in Advances in the theory of shock waves, pages 259\u2013305, (2001)","DOI":"10.1007\/978-1-4612-0193-9_4"},{"issue":"3","key":"2972_CR36","doi-asserted-by":"publisher","DOI":"10.1063\/1.2884710","volume":"49","author":"W-A Yong","year":"2008","unstructured":"Yong, W.-A.: An interesting class of partial differential equations. Journal of Mathematical Physics 49(3), 033503 (2008)","journal-title":"Journal of Mathematical Physics"},{"key":"2972_CR37","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s002050050188","volume":"150","author":"Y Zeng","year":"1999","unstructured":"Zeng, Y.: Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation. Archive for rational mechanics and analysis 150, 225\u2013279 (1999)","journal-title":"Archive for rational mechanics and analysis"},{"issue":"3","key":"2972_CR38","doi-asserted-by":"publisher","first-page":"609","DOI":"10.4310\/CMS.2017.v15.n3.a3","volume":"15","author":"W Zhao","year":"2017","unstructured":"Zhao, W., Yong, W.-A., Luo, L.-S.: Stability analysis of a class of globally hyperbolic moment system. Communications in Mathematical Sciences 15(3), 609\u2013633 (2017)","journal-title":"Communications in Mathematical Sciences"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02972-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-025-02972-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02972-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T00:09:46Z","timestamp":1757203786000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-025-02972-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,1]]},"references-count":38,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,8]]}},"alternative-id":["2972"],"URL":"https:\/\/doi.org\/10.1007\/s10915-025-02972-4","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2025,7,1]]},"assertion":[{"value":"9 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 June 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 July 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"60"}}