{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T22:29:49Z","timestamp":1781735389235,"version":"3.54.5"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,1,27]],"date-time":"2016-01-27T00:00:00Z","timestamp":1453852800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,27]],"date-time":"2016-01-27T00:00:00Z","timestamp":1453852800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000181","name":"AFOSR","doi-asserted-by":"crossref","award":["FA9550-12-1-0224"],"award-info":[{"award-number":["FA9550-12-1-0224"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000181","name":"AFOSR","doi-asserted-by":"crossref","award":["FA9550-12-1-0343"],"award-info":[{"award-number":["FA9550-12-1-0343"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000181","name":"AFOSR","doi-asserted-by":"crossref","award":["FA9550-12-1-0455"],"award-info":[{"award-number":["FA9550-12-1-0455"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-15-1-0235"],"award-info":[{"award-number":["FA9550-15-1-0235"]}],"id":[{"id":"10.13039\/100000181","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":[[2016,9]]},"DOI":"10.1007\/s10915-016-0164-2","type":"journal-article","created":{"date-parts":[[2016,1,27]],"date-time":"2016-01-27T05:50:20Z","timestamp":1453873820000},"page":"914-942","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":52,"title":["Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes"],"prefix":"10.1007","volume":"68","author":[{"given":"Andrew J.","family":"Christlieb","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sigal","family":"Gottlieb","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zachary","family":"Grant","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David C.","family":"Seal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,1,27]]},"reference":[{"key":"164_CR1","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1006\/jcph.2000.6443","volume":"160","author":"DS Balsara","year":"2000","unstructured":"Balsara, D.S., Shu, C.-W.: Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comput. Phys. 160, 405\u2013452 (2000)","journal-title":"J. Comput. Phys."},{"key":"164_CR2","unstructured":"Bresten, C., Gottlieb, S., Grant, Z., Higgs, D., Ketcheson, D.I., N\u00e9meth, A.: Strong stability preserving multistep Runge\u2013Kutta methods. Accept. Publ. Math. Comput"},{"key":"164_CR3","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/s11075-009-9349-1","volume":"53","author":"RPK Chan","year":"2010","unstructured":"Chan, R.P.K., Tsai, A.Y.J.: On explicit two-derivative Runge\u2013Kutta methods. Numer. Algorithms 53, 171\u2013194 (2010)","journal-title":"Numer. Algorithms"},{"key":"164_CR4","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1137\/S0036142902415584","volume":"42","author":"L Ferracina","year":"2004","unstructured":"Ferracina, L., Spijker, M.N.: Stepsize restrictions for the total-variation-diminishing property in general Runge\u2013Kutta methods. SIAM J. Numer. Anal. 42, 1073\u20131093 (2004)","journal-title":"SIAM J. Numer. Anal."},{"key":"164_CR5","first-page":"201","volume":"249","author":"L Ferracina","year":"2005","unstructured":"Ferracina, L., Spijker, M.N.: An extension and analysis of the Shu\u2013Osher representation of Runge\u2013Kutta methods. Math. Comput. 249, 201\u2013219 (2005)","journal-title":"Math. Comput."},{"key":"164_CR6","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/BF01390429","volume":"50","author":"E Gekeler","year":"1986","unstructured":"Gekeler, E., Widmann, R.: On the order conditions of Runge\u2013Kutta methods with higher derivatives. Numer. Math. 50, 183\u2013203 (1986)","journal-title":"Numer. Math."},{"key":"164_CR7","doi-asserted-by":"publisher","DOI":"10.1142\/7498","volume-title":"Strong Stability Preserving Runge\u2013Kutta and Multistep Time Discretizations","author":"S Gottlieb","year":"2011","unstructured":"Gottlieb, S., Ketcheson, D.I., Shu, C.-W.: Strong Stability Preserving Runge\u2013Kutta and Multistep Time Discretizations. World Scientific Press, Singapore (2011)"},{"key":"164_CR8","unstructured":"Grant, Z.J.: Explicit SSP multistage two-derivative SSP optimization code. \n                    https:\/\/github.com\/SSPmethods\/SSPMultiStageTwoDerivativeMethods\n                    \n                   (2015)"},{"key":"164_CR9","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/0021-9991(87)90031-3","volume":"71","author":"A Harten","year":"1987","unstructured":"Harten, A., Engquist, B., Osher, S., Chakravarthy, S.R.: Uniformly high-order accurate essentially nonoscillatory schemes. III. J. Comput. Phys. 71, 231\u2013303 (1987)","journal-title":"III. J. Comput. Phys."},{"key":"164_CR10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511618352","volume-title":"Spectral Methods for Time Dependent Problems","author":"J Hesthaven","year":"2007","unstructured":"Hesthaven, J., Gottlieb, S., Gottlieb, D.: Spectral Methods for Time Dependent Problems. Cambridge University Press, Cambridge Monographs of Applied and Computational Mathematics, Cambridge (2007)"},{"key":"164_CR11","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1023\/B:JOMP.0000030075.59237.61","volume":"21","author":"I Higueras","year":"2004","unstructured":"Higueras, I.: On strong stability preserving time discretization methods. J. Sci. Comput. 21, 193\u2013223 (2004)","journal-title":"J. Sci. Comput."},{"key":"164_CR12","doi-asserted-by":"publisher","first-page":"924","DOI":"10.1137\/S0036142903427068","volume":"43","author":"I Higueras","year":"2005","unstructured":"Higueras, I.: Representations of Runge\u2013Kutta methods and strong stability preserving methods. SIAM J. Numer. Anal. 43, 924\u2013948 (2005)","journal-title":"SIAM J. Numer. Anal."},{"key":"164_CR13","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1006\/jcph.1996.0130","volume":"126","author":"G-S Jiang","year":"1996","unstructured":"Jiang, G.-S., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202\u2013228 (1996)","journal-title":"J. Comput. Phys."},{"key":"164_CR14","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/BF02241605","volume":"9","author":"K Kastlunger","year":"1972","unstructured":"Kastlunger, K., Wanner, G.: On Turan type implicit Runge\u2013Kutta methods. Comput. (Arch. Elektron. Rechnen) 9, 317\u2013325 (1972). doi:\n                    10.1007\/BF02241605","journal-title":"Comput. (Arch. Elektron. Rechnen)"},{"key":"164_CR15","first-page":"9","volume":"9","author":"KH Kastlunger","year":"1972","unstructured":"Kastlunger, K.H., Wanner, G.: Runge Kutta processes with multiple nodes. Comput. (Arch. Elektron. Rechnen) 9, 9\u201324 (1972)","journal-title":"Comput. (Arch. Elektron. Rechnen)"},{"key":"164_CR16","doi-asserted-by":"publisher","first-page":"2113","DOI":"10.1137\/07070485X","volume":"30","author":"DI Ketcheson","year":"2008","unstructured":"Ketcheson, D.I.: Highly efficient strong stability preserving Runge\u2013Kutta methods with low-storage implementations. SIAM J. Sci. Comput. 30, 2113\u20132136 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"164_CR17","unstructured":"Ketcheson, D.I., Gottlieb, S., Macdonald, C.B.: Strong stability preserving two-step Runge-Kutta methods. SIAM J. Numer. Anal. 49, 2618\u20132639 (2012)"},{"key":"164_CR18","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1016\/j.apnum.2008.03.034","volume":"52","author":"DI Ketcheson","year":"2009","unstructured":"Ketcheson, D.I., Macdonald, C.B., Gottlieb, S.: Optimal implicit strong stability preserving Runge\u2013Kutta methods. Appl. Numer. Math. 52, 373 (2009)","journal-title":"Appl. Numer. Math."},{"key":"164_CR19","unstructured":"Ketcheson, D.I., Parsani, M., Ahmadia, A.J.: Rk-opt: software for the design of Runge\u2013Kutta methods, version 0.2. \n                    https:\/\/github.com\/ketch\/RK-opt"},{"key":"164_CR20","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1007\/BF01933264","volume":"31","author":"JFBM Kraaijevanger","year":"1991","unstructured":"Kraaijevanger, J.F.B.M.: Contractivity of Runge\u2013Kutta methods. BIT 31, 482\u2013528 (1991)","journal-title":"BIT"},{"key":"164_CR21","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1002\/cpa.3160130205","volume":"13","author":"P Lax","year":"1960","unstructured":"Lax, P., Wendroff, B.: Systems of conservation laws. Commun. Pure Appl. Math. 13, 217\u2013237 (1960)","journal-title":"Commun. Pure Appl. Math."},{"key":"164_CR22","doi-asserted-by":"publisher","first-page":"325","DOI":"10.2977\/prims\/1195184026","volume":"18","author":"T Mitsui","year":"1982","unstructured":"Mitsui, T.: Runge\u2013Kutta type integration formulas including the evaluation of the second derivative. i. Publ. Res. Inst. Math. Sci. 18, 325\u2013364 (1982)","journal-title":"Publ. Res. Inst. Math. Sci."},{"key":"164_CR23","first-page":"95","volume":"45","author":"T Nguyen-Ba","year":"2010","unstructured":"Nguyen-Ba, T., Nguyen-Thu, H., Giordano, T., Vaillancourt, R.: One-step strong-stability-preserving Hermite\u2013Birkhoff\u2013Taylor methods. Sci. J. Riga Tech. Univ. 45, 95\u2013104 (2010)","journal-title":"Sci. J. Riga Tech. Univ."},{"key":"164_CR24","unstructured":"Obreschkoff, N.: Neue Quadraturformeln. Abh. Preuss. Akad. Wiss. Math. Nat. Kl. 4 (1940)"},{"key":"164_CR25","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/BF03167588","volume":"21","author":"H Ono","year":"2004","unstructured":"Ono, H., Yoshida, T.: Two-stage explicit Runge\u2013Kutta type methods using derivatives. Jpn. J. Ind. Appl. Math. 21, 361\u2013374 (2004)","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"164_CR26","doi-asserted-by":"publisher","first-page":"4528","DOI":"10.1016\/j.cma.2004.11.007","volume":"194","author":"J Qiu","year":"2005","unstructured":"Qiu, J., Dumbser, M., Shu, C.-W.: The discontinuous Galerkin method with Lax\u2013Wendroff type time discretizations. Comput. Methods Appl. Mech. Eng. 194, 4528\u20134543 (2005)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"164_CR27","doi-asserted-by":"publisher","first-page":"2185","DOI":"10.1137\/S1064827502412504","volume":"24","author":"J Qiu","year":"2003","unstructured":"Qiu, J., Shu, C.-W.: Finite difference WENO schemes with Lax\u2013Wendroff-type time discretizations. SIAM J. Sci. Comput. 24, 2185\u20132198 (2003)","journal-title":"SIAM J. Sci. Comput."},{"key":"164_CR28","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1023\/A:1015156832269","volume":"17","author":"SJ Ruuth","year":"2002","unstructured":"Ruuth, S.J., Spiteri, R.J.: Two barriers on strong-stability-preserving time discretization methods. J. Sci. Comput. 17, 211\u2013220 (2002)","journal-title":"J. Sci. Comput."},{"key":"164_CR29","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/s10915-013-9787-8","volume":"60","author":"DC Seal","year":"2014","unstructured":"Seal, D.C., Guclu, Y., Christlieb, A.J.: High-order multiderivative time integrators for hyperbolic conservation laws. J. Sci. Comput. 60, 101\u2013140 (2014)","journal-title":"J. Sci. Comput."},{"key":"164_CR30","doi-asserted-by":"crossref","first-page":"349","DOI":"10.32917\/hmj\/1206137979","volume":"1","author":"H Shintani","year":"1971","unstructured":"Shintani, H.: On one-step methods utilizing the second derivative. Hiroshima Math. J. 1, 349\u2013372 (1971)","journal-title":"Hiroshima Math. J."},{"key":"164_CR31","doi-asserted-by":"crossref","first-page":"353","DOI":"10.32917\/hmj\/1206137626","volume":"2","author":"H Shintani","year":"1972","unstructured":"Shintani, H.: On explicit one-step methods utilizing the second derivative. Hiroshima Math. J. 2, 353\u2013368 (1972)","journal-title":"Hiroshima Math. J."},{"key":"164_CR32","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1137\/0909073","volume":"9","author":"C-W Shu","year":"1988","unstructured":"Shu, C.-W.: Total-variation diminishing time discretizations. SIAM J. Sci. Stat. Comp. 9, 1073\u20131084 (1988)","journal-title":"SIAM J. Sci. Stat. Comp."},{"key":"164_CR33","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1016\/0021-9991(88)90177-5","volume":"77","author":"C-W Shu","year":"1988","unstructured":"Shu, C.-W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439\u2013471 (1988)","journal-title":"J. Comput. Phys."},{"key":"164_CR34","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1137\/S0036142901389025","volume":"40","author":"RJ Spiteri","year":"2002","unstructured":"Spiteri, R.J., Ruuth, S.J.: A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal. 40, 469\u2013491 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"164_CR35","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1090\/S0025-5718-1963-0157485-3","volume":"17","author":"DD Stancu","year":"1963","unstructured":"Stancu, D.D., Stroud, A.H.: Quadrature formulas with simple Gaussian nodes and multiple fixed nodes. Math. Comp. 17, 384\u2013394 (1963)","journal-title":"Math. Comp."},{"key":"164_CR36","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1098\/rspa.2001.0926","volume":"458","author":"E Toro","year":"2002","unstructured":"Toro, E., Titarev, V.: Solution of the generalized Riemann problem for advection-reaction equations. Eng. Sci. Proc. R. Soc. Lond. A Math. Phys. 458, 271\u2013281 (2002)","journal-title":"Eng. Sci. Proc. R. Soc. Lond. A Math. Phys."},{"key":"164_CR37","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1007\/s11075-014-9823-2","volume":"65","author":"AYJ Tsai","year":"2014","unstructured":"Tsai, A.Y.J., Chan, R.P.K., Wang, S.: Two-derivative Runge\u2013Kutta methods for PDEs using a novel discretization approach. Numer. Algorithms 65, 687\u2013703 (2014)","journal-title":"Numer. Algorithms"},{"key":"164_CR38","first-page":"30","volume":"12","author":"P Tur\u00e1n","year":"1950","unstructured":"Tur\u00e1n, P.: On the theory of the mechanical quadrature. Acta Sci. Math. Szeged 12, 30\u201337 (1950)","journal-title":"Acta Sci. Math. Szeged"}],"updated-by":[{"DOI":"10.1007\/s10915-016-0195-8","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2016,3,23]],"date-time":"2016-03-23T00:00:00Z","timestamp":1458691200000}}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0164-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0164-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0164-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0164-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T09:18:29Z","timestamp":1589707109000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0164-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,27]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,9]]}},"alternative-id":["164"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0164-2","relation":{"correction":[{"id-type":"doi","id":"10.1007\/s10915-016-0195-8","asserted-by":"object"}]},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,27]]},"assertion":[{"value":"28 April 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 December 2015","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 January 2016","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2016","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}