{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:17:59Z","timestamp":1759940279408,"version":"3.41.0"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,9,1]],"date-time":"2016-09-01T00:00:00Z","timestamp":1472688000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,3]]},"DOI":"10.1007\/s10915-016-0273-y","type":"journal-article","created":{"date-parts":[[2016,9,2]],"date-time":"2016-09-02T19:41:03Z","timestamp":1472845263000},"page":"1105-1143","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Accurate Implicit\u2013Explicit General Linear Methods with Inherent Runge\u2013Kutta Stability"],"prefix":"10.1007","volume":"70","author":[{"given":"Micha\u0142","family":"Bra\u015b","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1412-8702","authenticated-orcid":false,"given":"Giuseppe","family":"Izzo","sequence":"additional","affiliation":[]},{"given":"Zdzis\u0142aw","family":"Jackiewicz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,9,1]]},"reference":[{"key":"273_CR1","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1016\/j.jcp.2013.02.009","volume":"242","author":"A Abdulle","year":"2013","unstructured":"Abdulle, A., Vilmart, G.: PIROCK: a swiss-knife partitioned implicit\u2013explicit orthogonal Runge\u2013Kutta\u2013Chebyshev integrator for stiff diffusion\u2013advection\u2013reaction problems with or without noise. J. Comput. Phys. 242, 869\u2013888 (2013)","journal-title":"J. Comput. Phys."},{"key":"273_CR2","doi-asserted-by":"crossref","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\u2013explicit Runge\u2013Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25, 151\u2013167 (1997)","journal-title":"Appl. Numer. Math."},{"key":"273_CR3","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1137\/0732037","volume":"32","author":"UM Ascher","year":"1995","unstructured":"Ascher, U.M., Ruuth, S.J., Wetton, B.: Implicit\u2013explicit methods for time dependent PDE\u2019s. SIAM J. Numer. Anal. 32, 797\u2013823 (1995)","journal-title":"SIAM J. Numer. Anal."},{"key":"273_CR4","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s12190-011-0485-0","volume":"38","author":"S Beck","year":"2012","unstructured":"Beck, S., Weiner, R., Podhaisky, H., Schmitt, B.A.: Implicit peer methods for large stiff ODE systems. J. Appl. Math. Comput. 38, 389\u2013406 (2012)","journal-title":"J. Appl. Math. Comput."},{"key":"273_CR5","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1137\/060656929","volume":"45","author":"S Boscarino","year":"2007","unstructured":"Boscarino, S.: Error analysis of IMEX Runge\u2013Kutta methods derived from differential\u2013algebraic systems. SIAM J. Numer. Anal. 45, 1600\u20131621 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"273_CR6","doi-asserted-by":"crossref","unstructured":"Boscarino, S.: On the accurate third order implicit\u2013explicit Runge\u2013Kutta methods for stiff problems. Appl. Numer. Math. 59, 1515\u20131528.37 (2009), B305\u2013B331 (2015)","DOI":"10.1016\/j.apnum.2008.10.003"},{"key":"273_CR7","doi-asserted-by":"publisher","unstructured":"Boscarino, S., B\u00fcrger, R., Mulet, P., Russo, G., Villada, M.L.: Linearly implicit IMEX Runge\u2013Kutta methods for a class of degenerate convection\u2013diffusion problems. SIAM J. Sci. Comput. 37, B305\u2013B331 (2015). doi: 10.1137\/140967544","DOI":"10.1137\/140967544"},{"key":"273_CR8","doi-asserted-by":"crossref","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\u2013Kutta schemes and applications to hyperbolic systems with relaxation. SIAM J. Sci. Comput. 31, 1926\u20131945 (2009)","journal-title":"SIAM J. Sci. Comput."},{"key":"273_CR9","unstructured":"Bra\u015b, M., Cardone, A., Jackiewicz, Z., Welfert, B.: Order reduction phenomenon for general linear methods. SIAM J. Number. Anal. (submitted)"},{"key":"273_CR10","volume-title":"The Numerical Analysis of Ordinary Differential Equations. Runge\u2013Kutta and General Linear Methods","author":"JC Butcher","year":"1987","unstructured":"Butcher, J.C.: The Numerical Analysis of Ordinary Differential Equations. Runge\u2013Kutta and General Linear Methods. Wiley, Chichester (1987)"},{"key":"273_CR11","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/0168-9274(93)90059-Z","volume":"11","author":"JC Butcher","year":"1993","unstructured":"Butcher, J.C.: Diagonally-implicit multi-stage integration methods. Appl. Numer. Math. 11, 347\u2013363 (1993)","journal-title":"Appl. Numer. Math."},{"key":"273_CR12","doi-asserted-by":"crossref","DOI":"10.1002\/0470868279","volume-title":"Numerical Methods for Ordinary Differential Equations","author":"JC Butcher","year":"2003","unstructured":"Butcher, J.C.: Numerical Methods for Ordinary Differential Equations. Wiley, Chichester (2003)"},{"key":"273_CR13","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1017\/S0962492906220014","volume":"15","author":"JC Butcher","year":"2006","unstructured":"Butcher, J.C.: General linear methods. Acta Numer. 15, 157\u2013256 (2006)","journal-title":"Acta Numer."},{"key":"273_CR14","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1007\/BF01990528","volume":"33","author":"JC Butcher","year":"1993","unstructured":"Butcher, J.C., Jackiewicz, Z.: Diagonally implicit general linear methods for ordinary differential equations. BIT 33, 452\u2013472 (1993)","journal-title":"BIT"},{"key":"273_CR15","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1023\/B:NUMA.0000027738.54515.50","volume":"36","author":"JC Butcher","year":"2004","unstructured":"Butcher, J.C., Jackiewicz, Z.: Construction of general linear methods with Runge\u2013Kutta stability properties. Numer. Algorithms 36, 53\u201372 (2004)","journal-title":"Numer. Algorithms"},{"key":"273_CR16","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1016\/j.jco.2007.01.009","volume":"23","author":"JC Butcher","year":"2007","unstructured":"Butcher, J.C., Jackiewicz, Z., Wright, W.M.: Error propagation for general linear methods for ordinary differential equations. J. Complex. 23, 560\u2013580 (2007)","journal-title":"J. Complex."},{"key":"273_CR17","doi-asserted-by":"crossref","first-page":"695","DOI":"10.1023\/B:BITN.0000009952.71388.23","volume":"43","author":"JC Butcher","year":"2003","unstructured":"Butcher, J.C., Wright, W.M.: The construction of practical general linear methods. BIT 43, 695\u2013721 (2003)","journal-title":"BIT"},{"key":"273_CR18","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/S0168-9274(00)00061-1","volume":"37","author":"MP Calvo","year":"2001","unstructured":"Calvo, M.P., de Frutos, J., Novo, J.: Linearly implicit Runge\u2013Kutta methods for advection\u2013diffusion\u2013reaction problems. Appl. Numer. Math. 37, 535\u2013549 (2001)","journal-title":"Appl. Numer. Math."},{"key":"273_CR19","unstructured":"Cardone, A., Jackiewicz, Z., Sandu, A., Zhang, H.: Extrapolation-based implicit\u2013explicit general linear methods (2013), arXiv:1304.2276"},{"key":"273_CR20","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/s11075-013-9759-y","volume":"65","author":"A Cardone","year":"2014","unstructured":"Cardone, A., Jackiewicz, Z., Sandu, A., Zhang, H.: Extrapolation-based implicit\u2013explicit general linear methods. Numer. Algorithms 65, 377\u2013399 (2014)","journal-title":"Numer. Algorithms"},{"key":"273_CR21","doi-asserted-by":"crossref","first-page":"18","DOI":"10.3846\/13926292.2014.892903","volume":"19","author":"A Cardone","year":"2014","unstructured":"Cardone, A., Jackiewicz, Z., Sandu, A., Zhang, H.: Extrapolated implicit\u2013explicit Runge\u2013Kutta methods. Math. Model. Anal. 19, 18\u201343 (2014)","journal-title":"Math. Model. Anal."},{"key":"273_CR22","doi-asserted-by":"crossref","unstructured":"Cardone, A., Jackiewicz, Z., Sandu, A., Zhang, H.: Construction of highly stable implicit-explicit general linear methods. In: Discrete and Continuous Dynamical Systems. Series S, vol. 2015, pp. 185\u2013194 (2015)","DOI":"10.3934\/proc.2015.0185"},{"key":"273_CR23","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/BF01396412","volume":"35","author":"M Crouzeix","year":"1980","unstructured":"Crouzeix, M.: Une m\u00e9thode multipas implicite-explicite pour l\u2019approximation des \u00e9quations d\u2019\u00e9volution paraboliques. Numer. Math. 35, 257\u2013276 (1980)","journal-title":"Numer. Math."},{"key":"273_CR24","volume-title":"Fourier Series and Integrals","author":"H Dym","year":"1972","unstructured":"Dym, H., McKean, H.P.: Fourier Series and Integrals. Academic Press, New York (1972)"},{"key":"273_CR25","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0168-9274(97)00059-7","volume":"25","author":"J Frank","year":"1997","unstructured":"Frank, J., Hundsdorfer, W., Verwer, J.G.: On the stability of implicit\u2013explicit linear multistep methods. Appl. Numer. Math. 25, 193\u2013205 (1997)","journal-title":"Appl. Numer. Math."},{"key":"273_CR26","volume-title":"Solving Ordinary Differential Equations I: Nonstiff Problems","author":"E Hairer","year":"1993","unstructured":"Hairer, E., N\u00f8rsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems. Springer, New York (1993)"},{"key":"273_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05221-7","volume-title":"Solving Ordinary Differential Equations II. Stiff and Differential\u2013Algebraic Problems","author":"E Hairer","year":"1996","unstructured":"Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Stiff and Differential\u2013Algebraic Problems. Springer, Berlin (1996)"},{"key":"273_CR28","doi-asserted-by":"crossref","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, 2016\u20132042 (2007)","journal-title":"J. Comput. Phys."},{"key":"273_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-09017-6","volume-title":"Numerical Solution of Time-Dependent Advection\u2013Diffusion\u2013Reaction Equations","author":"W Hundsdorfer","year":"2003","unstructured":"Hundsdorfer, W., Verwer, J.G.: Numerical Solution of Time-Dependent Advection\u2013Diffusion\u2013Reaction Equations. Springer, Berlin, Heidelberg, New York (2003)"},{"key":"273_CR30","doi-asserted-by":"crossref","unstructured":"Izzo, G., Jackiewicz, Z.: Highly stable implicit\u2013explicit Runge\u2013Kutta methods. Appl. Number. Math. (submitted)","DOI":"10.1016\/j.apnum.2016.10.018"},{"key":"273_CR31","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/S0168-9274(01)00154-4","volume":"42","author":"Z Jackiewicz","year":"2002","unstructured":"Jackiewicz, Z.: Implementation of DIMSIMs for stiff differential systems. Appl. Numer. Math. 42, 251\u2013267 (2002)","journal-title":"Appl. Numer. Math."},{"key":"273_CR32","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s10915-004-4631-9","volume":"25","author":"Z Jackiewicz","year":"2005","unstructured":"Jackiewicz, Z.: Construction and implementation of general linear methods for ordinary differential equations. A review. J. Sci. Comput. 25, 29\u201349 (2005)","journal-title":"J. Sci. Comput."},{"key":"273_CR33","doi-asserted-by":"crossref","DOI":"10.1002\/9780470522165","volume-title":"General Linear Methods for Ordinary Differential Equations","author":"Z Jackiewicz","year":"2009","unstructured":"Jackiewicz, Z.: General Linear Methods for Ordinary Differential Equations. Wiley, Hoboken (2009)"},{"key":"273_CR34","doi-asserted-by":"crossref","first-page":"4955","DOI":"10.1016\/j.jcp.2011.03.015","volume":"230","author":"S Jebens","year":"2011","unstructured":"Jebens, S., Knoth, O., Weiner, R.: Partially implicit peer methods for the compressible Euler equations. J. Comput. Phys. 230, 4955\u20134974 (2011)","journal-title":"J. Comput. Phys."},{"key":"273_CR35","doi-asserted-by":"crossref","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\u2013Kutta schemes for convection\u2013diffusion\u2013reaction equations. Appl. Numer. Math. 44, 139\u2013181 (2003)","journal-title":"Appl. Numer. Math."},{"key":"273_CR36","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s10543-005-0016-1","volume":"45","author":"AT Layton","year":"2005","unstructured":"Layton, A.T., Minion, M.L.: Implications of the choice of quadrature nodes for Picard integral deferred correction methods for ordinary differential equations. BIT 45, 341\u2013373 (2005)","journal-title":"BIT"},{"key":"273_CR37","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.apnum.2003.11.005","volume":"48","author":"ML Minion","year":"2004","unstructured":"Minion, M.L.: Semi-implicit projection methods for incompressible flow based on spectral deferred corrections. Appl. Numer. Math. 48, 369\u2013387 (2004)","journal-title":"Appl. Numer. Math."},{"key":"273_CR38","unstructured":"Pareschi, L., Russo, G.: Implicit\u2013explicit Runge\u2013Kutta schemes for stiff systems of differential equations. Recent trends in numerical analysis, 269\u2013288, Adv. Theory Comput. Math., 3, Nova Science Publishers, Huntington, NY (2001)"},{"key":"273_CR39","first-page":"129","volume":"25","author":"L Pareschi","year":"2005","unstructured":"Pareschi, L., Russo, G.: Implicit\u2013explicit Runge\u2013Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput. 25, 129\u2013155 (2005)","journal-title":"J. Sci. Comput."},{"key":"273_CR40","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1126\/science.261.5118.189","volume":"261","author":"JE Pearson","year":"1993","unstructured":"Pearson, J.E.: Complex patterns in a simple systems. Science 261, 189\u2013192 (1993)","journal-title":"Science"},{"key":"273_CR41","doi-asserted-by":"crossref","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. Math. Comput. 28, 145\u2013162 (1974)","journal-title":"Math. Comput."},{"key":"273_CR42","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1016\/j.cam.2005.09.014","volume":"196","author":"LF Shampine","year":"2006","unstructured":"Shampine, L.F., Sommeijer, B.P., Verwer, J.G.: IRKC: an IMEX solver for stiff diffusion\u2013reaction PDEs. J. Comput. Appl. Math. 196, 485\u2013497 (2006)","journal-title":"J. Comput. Appl. Math."},{"key":"273_CR43","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/0022-5193(79)90042-0","volume":"81","author":"J Schnakenberg","year":"1979","unstructured":"Schnakenberg, J.: Simple chemical reaction systems with limiting cycle behaviour. J. Theor. Biol. 81, 389\u2013400 (1979)","journal-title":"J. Theor. Biol."},{"key":"273_CR44","first-page":"439","volume-title":"High-Order Methods for Computational Physics. Lecture Notes in Computational Science and Engineering","author":"C-W Shu","year":"1999","unstructured":"Shu, C.-W.: High order ENO and WENO schemes for computational fluid dynamics. In: Barth, T.J., Deconinck, H. (eds.) High-Order Methods for Computational Physics. Lecture Notes in Computational Science and Engineering, vol. 9, pp. 439\u2013582. Springer, Berlin (1999)"},{"key":"273_CR45","doi-asserted-by":"crossref","first-page":"1871","DOI":"10.1137\/050637868","volume":"45","author":"R Wang","year":"2007","unstructured":"Wang, R., Spiteri, R.J.: Linear instability of the fifth-order WENO method. SIAM J. Numer. Anal. 45, 1871\u20131901 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"273_CR46","unstructured":"Wright, W.: General linear methods with inherent Runge\u2013Kutta stability, Ph.D. thesis, The University of Auckland, New Zealand (2002)"},{"key":"273_CR47","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1023\/A:1021195804379","volume":"31","author":"W Wright","year":"2002","unstructured":"Wright, W.: Explicit general linear methods with inherent Runge\u2013Kutta stability. Numer. Algorithms 31, 381\u2013399 (2002)","journal-title":"Numer. Algorithms"},{"key":"273_CR48","first-page":"4","volume-title":"Towards a Theoretical Biology","author":"EC Zeeman","year":"1972","unstructured":"Zeeman, E.C.: Differential Equations for the Heartbeat and Nerve Impulse. In: Waddington, C.H. (ed.) Towards a Theoretical Biology, vol. 4, pp. 4\u201367. Edinburgh University Press, Edinburgh (1972)"},{"key":"273_CR49","unstructured":"Zhang, H., Sandu, A., Blaise, S.: High order implicit\u2013explicit general linear methods with optimized stability regions (2014), arXiv:1407.2337"},{"key":"273_CR50","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s10915-014-9819-z","volume":"61","author":"H Zhang","year":"2014","unstructured":"Zhang, H., Sandu, A., Blaise, S.: Partitioned and implicit\u2013explicit general linear methods for ordinary differential equations. J. Sci. Comput. 61, 119\u2013144 (2014)","journal-title":"J. Sci. Comput."},{"key":"273_CR51","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1137\/130937883","volume":"53","author":"E Zharovsky","year":"2015","unstructured":"Zharovsky, E., Sandu, A., Zhang, H.: A class of implicit\u2013explicit two-step Runge\u2013Kutta methods. SIAM J. Numer. Anal. 53, 321\u2013341 (2015)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0273-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0273-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0273-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0273-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,10]],"date-time":"2025-06-10T16:33:12Z","timestamp":1749573192000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0273-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,1]]},"references-count":51,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["273"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0273-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2016,9,1]]}}}