{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T18:00:28Z","timestamp":1784916028447,"version":"3.55.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,10,29]],"date-time":"2013-10-29T00:00:00Z","timestamp":1383004800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2014,8]]},"DOI":"10.1007\/s10915-013-9796-7","type":"journal-article","created":{"date-parts":[[2013,10,28]],"date-time":"2013-10-28T08:59:15Z","timestamp":1382950755000},"page":"313-344","source":"Crossref","is-referenced-by-count":62,"title":["Optimal Strong-Stability-Preserving Runge\u2013Kutta Time Discretizations for Discontinuous Galerkin Methods"],"prefix":"10.1007","volume":"60","author":[{"given":"Ethan J.","family":"Kubatko","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjamin A.","family":"Yeager","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David I.","family":"Ketcheson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2013,10,29]]},"reference":[{"key":"9796_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/9780470753767","volume-title":"Numerical Methods for Ordinary Differential Equations","author":"JC Butcher","year":"2008","unstructured":"Butcher, J.C.: Numerical Methods for Ordinary Differential Equations, 2nd edn. Wiley, Hoboken, NJ (2008)","edition":"2"},{"key":"9796_CR2","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.jcp.2012.12.019","volume":"238","author":"Y Cheng","year":"2013","unstructured":"Cheng, Y., Li, F., Qiu, J., Xu, L.: Positivity-preserving DG and central DG methods for ideal MHD equations. J. Comput. Phys. 238, 255\u2013280 (2013)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"9796_CR3","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1051\/m2an\/1991250303371","volume":"25","author":"B Cockburn","year":"1989","unstructured":"Cockburn, B., Shu, C.W.: The Runge\u2013Kutta local projection $${P}^1$$ P 1 -discontinuous Galerkin finite element method for scalar conservation laws. Math. Model. Numer. Anal. 25(3), 337\u2013361 (1989)","journal-title":"Math. Model. Numer. Anal."},{"key":"9796_CR4","first-page":"411","volume":"52","author":"B Cockburn","year":"1989","unstructured":"Cockburn, B., Shu, C.W.: TVB Runge\u2013Kutta local projection discontinuous Galerkin finite element method for scalar conservation laws II: general framework. Math. Comput. 52, 411\u2013435 (1989)","journal-title":"Math. Comput."},{"issue":"3","key":"9796_CR5","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."},{"key":"9796_CR6","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s10915-007-9151-y","volume":"33","author":"EM Constantinescu","year":"2007","unstructured":"Constantinescu, E.M.: Multirate timestepping methods. J. Sci. Comput. 33, 239\u2013278 (2007)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"9796_CR7","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1016\/j.cma.2013.03.015","volume":"259","author":"C Dawson","year":"2013","unstructured":"Dawson, C., Trahan, C.J., Kubatko, E.J., Westerink, J.J.: A parallel local timestepping Runge\u2013Kutta discontinuous Galerkin method with applications to coastal ocean modeling. Comput. Methods Appl. Mech. Eng. 259(1), 154\u2013165 (2013)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9796_CR8","doi-asserted-by":"crossref","DOI":"10.1142\/7498","volume-title":"Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations","author":"S Gottlieb","year":"2011","unstructured":"Gottlieb, S., Ketcheson, D., Shu, C.W.: Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations. World Scientific, Singapore (2011)"},{"key":"9796_CR9","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1090\/S0025-5718-98-00913-2","volume":"67","author":"S Gottlieb","year":"1998","unstructured":"Gottlieb, S., Shu, C.W.: Total variation diminishing Runge\u2013Kutta schemes. Math. Comput. 67, 73\u201385 (1998)","journal-title":"Math. Comput."},{"issue":"1","key":"9796_CR10","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1023\/A:1020338228736","volume":"18","author":"S Gottlieb","year":"2003","unstructured":"Gottlieb, S., Shu, C.W.: Strong stability preserving properties of Runge\u2013Kutta time discretization methods for linear constant coefficient operators. J. Sci. Comput. 18(1), 83\u2013109 (2003)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"9796_CR11","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1137\/S003614450036757X","volume":"43","author":"S Gottlieb","year":"2001","unstructured":"Gottlieb, S., Shu, C.W., Tadmor, E.: Strong stability-preserving high-order time discretization methods. SIAM Rev. 43(1), 89\u2013112 (2001)","journal-title":"SIAM Rev."},{"key":"9796_CR12","unstructured":"Grant, M., Boyd, S.: Graph implementations for nonsmooth convex programs. In: Blondel, V., Boyd, S., Kimura, H. (eds.) Recent Advances in Learning and Control, Lecture Notes in Control and Information Sciences, pp. 95\u2013110. Springer, Berlin (2008). http:\/\/stanford.edu\/boyd\/~graph_dcp.html"},{"key":"9796_CR13","unstructured":"Grant, M., Boyd, S.: CVX: Matlab Software for Disciplined Convex Programming, version 2.0 beta (2012). http:\/\/cvxr.com\/cvx"},{"key":"9796_CR14","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0021-9991(83)90136-5","volume":"49","author":"A Harten","year":"1983","unstructured":"Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357\u2013393 (1983)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"9796_CR15","doi-asserted-by":"crossref","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(3), 924\u2013948 (2005)","journal-title":"SIAM J. Numer. Anal."},{"key":"9796_CR16","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1007\/BF01932030","volume":"18","author":"R Jeltsch","year":"1978","unstructured":"Jeltsch, R., Nevanlinna, O.: Largest disk of stability of explicit Runge\u2013Kutta methods. BIT Numer. Math. 18, 500\u2013502 (1978)","journal-title":"BIT Numer. Math."},{"issue":"4","key":"9796_CR17","doi-asserted-by":"crossref","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(4), 2113\u20132136 (2008)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"9796_CR18","doi-asserted-by":"crossref","first-page":"247","DOI":"10.2140\/camcos.2012.7.247","volume":"7","author":"DI Ketcheson","year":"2013","unstructured":"Ketcheson, D.I., Ahmadia, A.: Optimal stability polynomials for numerical integration of initial value problems. Commun. Appl. Math. Comput. Sci. 7(2), 247\u2013271 (2013)","journal-title":"Commun. Appl. Math. Comput. Sci."},{"key":"9796_CR19","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0378-4754(84)90039-9","volume":"26","author":"IP Kinnmark","year":"1984","unstructured":"Kinnmark, I.P., Gray, W.G.: One step integration methods with maximum stability regions. Math. Comput. Simul. 26, 87\u201392 (1984)","journal-title":"Math. Comput. Simul."},{"key":"9796_CR20","doi-asserted-by":"crossref","first-page":"1766","DOI":"10.1016\/j.cma.2009.01.007","volume":"198","author":"EJ Kubatko","year":"2009","unstructured":"Kubatko, E.J., Bunya, S., Dawson, C., Westerink, J.J.: Dynamic p-adaptive Runge\u2013Kutta discontinuous Galerkin methods for the shallow water equations. Comput. Methods Appl. Mech. Eng. 198, 1766\u20131774 (2009)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9796_CR21","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1016\/j.jcp.2006.08.005","volume":"222","author":"EJ Kubatko","year":"2007","unstructured":"Kubatko, E.J., Westerink, J.J., Dawson, C.: Semidiscrete discontinuous Galerkin methods and stage exceeding order strong stability preserving Runge\u2013Kutta time discretizations. J. Comput. Phys. 222, 832\u2013848 (2007)","journal-title":"J. Comput. Phys."},{"key":"9796_CR22","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.cma.2010.08.004","volume":"200","author":"C Mirabito","year":"2011","unstructured":"Mirabito, C., Dawson, C., Kubatko, E.J., Westerink, J.J., Bunya, S.: Implementation of a discontinuous Galerkin morphological model on two-dimensional unstructured meshes. Comput. Methods Appl. Mech. Eng. 200, 189\u2013207 (2011)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9796_CR23","unstructured":"Parsani, M., Ketcheson, D.I.: Design of optimal explicit linearly stable strong stability preserving Runge\u2013Kutta schemes for the spectral difference method. In : International Conference on Spectral and High Order Methods (2012)"},{"issue":"2","key":"9796_CR24","doi-asserted-by":"crossref","first-page":"A957","DOI":"10.1137\/120885899","volume":"35","author":"M Parsani","year":"2013","unstructured":"Parsani, M., Ketcheson, D.I., Deconinck, W.: Optimized explicit Runge\u2013Kutta schemes for the spectral difference method applied to wave propagation problems. SIAM J. Sci. Comput. 35(2), A957\u2013A986 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"9796_CR25","doi-asserted-by":"crossref","unstructured":"Reddy, S.C., Trefethen, L.N.: Stability of the method of lines. Numerische Mathematik 62, 235\u2013267 (1992)","DOI":"10.1007\/BF01396228"},{"key":"9796_CR26","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1090\/S0025-5718-05-01772-2","volume":"75","author":"SJ Ruuth","year":"2006","unstructured":"Ruuth, S.J.: Global optimization of explicit strong-stability-preserving Runge\u2013Kutta methods. Math. Comput. 75, 183\u2013207 (2006)","journal-title":"Math. Comput."},{"key":"9796_CR27","doi-asserted-by":"crossref","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":"9796_CR28","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0378-4754(02)00179-9","volume":"62","author":"RJ Spiteri","year":"2003","unstructured":"Spiteri, R.J., Ruuth, S.J.: Non-linear evolution using optimal fourth-order strong-stability-preserving Runge\u2013Kutta methods. Math. Comput. Simul. 62, 125\u2013135 (2003)","journal-title":"Math. Comput. Simul."},{"issue":"3","key":"9796_CR29","first-page":"438","volume":"1","author":"T Sun","year":"2009","unstructured":"Sun, T., Qiu, J.: LWDG method for a multi-class traffic flow model on an inhomogeneous highway. Adv. Appl. Math. Mech. 1(3), 438\u2013450 (2009)","journal-title":"Adv. Appl. Math. Mech."},{"issue":"4","key":"9796_CR30","doi-asserted-by":"crossref","first-page":"2067","DOI":"10.1016\/j.jcp.2011.11.024","volume":"231","author":"T Toulorge","year":"2012","unstructured":"Toulorge, T., Desmet, W.: Optimal Runge\u2013Kutta schemes for discontinuous Galerkin space discretizations applied to wave propagation problems. J. Comput. Phys. 231(4), 2067\u20132091 (2012)","journal-title":"J. Comput. Phys."},{"key":"9796_CR31","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.cma.2012.01.002","volume":"217","author":"CJ Trahan","year":"2012","unstructured":"Trahan, C.J., Dawson, C.: Local time-stepping in Runge\u2013Kutta discontinuous Galerkin finite element methods applied to the shallow-water equations. Comput. Methods Appl. Mech. Eng. 217, 139\u2013152 (2012)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9796_CR32","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/BF01404404","volume":"20","author":"P Houwen van der","year":"1972","unstructured":"van der Houwen, P.: Explicit Runge\u2013Kutta formulas with increased stability boundaries. Numerische Mathematik 20, 149\u2013164 (1972)","journal-title":"Numerische Mathematik"},{"key":"9796_CR33","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0378-4754(83)90092-7","volume":"25","author":"R Vichnevetsky","year":"1983","unstructured":"Vichnevetsky, R.: New stability theorems concerning one-step numerical methods for ordinary differential equations. Math. Comput. Simul. 25, 199\u2013205 (1983)","journal-title":"Math. Comput. Simul."},{"key":"9796_CR34","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/0021-9991(80)90033-9","volume":"35","author":"JH Williamson","year":"1980","unstructured":"Williamson, J.H.: Low-storage Runge\u2013Kutta schemes. J. Comput. Phys. 35, 48\u201356 (1980)","journal-title":"J. Comput. Phys."},{"key":"9796_CR35","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.jcp.2005.10.005","volume":"214","author":"Y Xing","year":"2010","unstructured":"Xing, Y., Shu, C.W.: High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. J. Comput. Phys. 214, 567\u2013598 (2010)","journal-title":"J. Comput. Phys."},{"key":"9796_CR36","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.1016\/j.advwatres.2010.08.005","volume":"33","author":"Y Xing","year":"2010","unstructured":"Xing, Y., Zhang, X., Shu, C.W.: Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations. Adv. Water Resour. 33, 1476\u20131493 (2010)","journal-title":"Adv. Water Resour."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9796-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-013-9796-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9796-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,31]],"date-time":"2019-07-31T10:59:36Z","timestamp":1564570776000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-013-9796-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,29]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["9796"],"URL":"https:\/\/doi.org\/10.1007\/s10915-013-9796-7","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,29]]}}}