{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:30:00Z","timestamp":1778718600670,"version":"3.51.4"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,6,14]],"date-time":"2018-06-14T00:00:00Z","timestamp":1528934400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,6,14]],"date-time":"2018-06-14T00:00:00Z","timestamp":1528934400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1419003"],"award-info":[{"award-number":["DMS-1419003"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1419105"],"award-info":[{"award-number":["DMS-1419105"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1613905"],"award-info":[{"award-number":["CCF-1613905"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-12-1-0293-DEF"],"award-info":[{"award-number":["FA9550-12-1-0293-DEF"]}],"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":[[2019,1]]},"DOI":"10.1007\/s10915-018-0761-3","type":"journal-article","created":{"date-parts":[[2018,6,14]],"date-time":"2018-06-14T12:25:56Z","timestamp":1528979156000},"page":"167-201","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["EPIRK-W and EPIRK-K Time Discretization Methods"],"prefix":"10.1007","volume":"78","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4410-4499","authenticated-orcid":false,"given":"Mahesh","family":"Narayanamurthi","sequence":"first","affiliation":[]},{"given":"Paul","family":"Tranquilli","sequence":"additional","affiliation":[]},{"given":"Adrian","family":"Sandu","sequence":"additional","affiliation":[]},{"given":"Mayya","family":"Tokman","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,6,14]]},"reference":[{"issue":"2","key":"761_CR1","doi-asserted-by":"publisher","first-page":"488","DOI":"10.1137\/100788860","volume":"33","author":"AH Al-Mohy","year":"2011","unstructured":"Al-Mohy, A.H., Higham, N.J.: Computing the action of the matrix exponential, with an application to exponential integrators. SIAM J. Sci. Comput. 33(2), 488\u2013511 (2011)","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"761_CR2","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.1016\/0001-6160(79)90196-2","volume":"27","author":"SM Allen","year":"1979","unstructured":"Allen, S.M., Cahn, J.W.: A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metall. 27(6), 1085\u20131095 (1979). \n                    https:\/\/doi.org\/10.1016\/0001-6160(79)90196-2","journal-title":"Acta Metall."},{"issue":"4","key":"761_CR3","doi-asserted-by":"publisher","first-page":"1715","DOI":"10.1137\/040612683","volume":"43","author":"H Berland","year":"2005","unstructured":"Berland, H., Owren, B., Skaflestad, B.: B-series and order conditions for exponential integrators. SIAM J. Numer. Anal. 43(4), 1715\u20131727 (2005)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"761_CR4","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1145\/1206040.1206044","volume":"33","author":"H Berland","year":"2007","unstructured":"Berland, H., Skaflestad, B., Wright, W.M.: Expint\u2014a matlab package for exponential integrators. ACM Trans. Math. Softw. (TOMS) 33(1), 4 (2007)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"761_CR5","doi-asserted-by":"publisher","DOI":"10.1002\/9780470753767","volume-title":"Numerical Methods for Ordinary Differential Equations","author":"J Butcher","year":"2008","unstructured":"Butcher, J.: Numerical Methods for Ordinary Differential Equations, 2nd edn. Wiley, New York (2008). \n                    https:\/\/doi.org\/10.1002\/9780470753767","edition":"2"},{"key":"761_CR6","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1093\/imanum\/drn086","volume":"30","author":"J Butcher","year":"2010","unstructured":"Butcher, J.: Trees, B-series and exponential integrators. IMA J. Numer. Anal. 30, 131\u2013140 (2010)","journal-title":"IMA J. Numer. Anal."},{"issue":"3\u20134","key":"761_CR7","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1016\/j.apnum.2008.03.021","volume":"59","author":"M Caliari","year":"2009","unstructured":"Caliari, M., Ostermann, A.: Implementation of exponential rosenbrock-type integrators. Appl. Numer. Math. 59(3\u20134), 568\u2013581 (2009)","journal-title":"Appl. Numer. Math."},{"key":"761_CR8","unstructured":"D\u2019Augustine, A.F.: MATLODE: A MATLAB ODE solver and sensitivity analysis toolbox. Masters Thesis, Virginia Tech (2018)"},{"key":"761_CR9","volume-title":"Solving Ordinary Differential Equations I: Nonstiff Problems. Springer Series in Computational Mathematics","author":"E Hairer","year":"1993","unstructured":"Hairer, E., Norsett, S., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems. Springer Series in Computational Mathematics, vol. 8. Springer, Berlin (1993)"},{"key":"761_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-05221-7","volume-title":"Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer Series in Computational Mathematics","author":"E Hairer","year":"1996","unstructured":"Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer Series in Computational Mathematics, vol. 14, 2nd edn. Springer, Berlin (1996)","edition":"2"},{"issue":"7","key":"761_CR11","doi-asserted-by":"publisher","first-page":"981","DOI":"10.1016\/j.apnum.2005.09.001","volume":"56","author":"W Heineken","year":"2006","unstructured":"Heineken, W., Warnecke, G.: Partitioning methods for reaction\u2013diffusion problems. Appl. Numer. Math. 56(7), 981\u20131000 (2006)","journal-title":"Appl. Numer. Math."},{"issue":"5","key":"761_CR12","doi-asserted-by":"publisher","first-page":"1911","DOI":"10.1137\/S0036142995280572","volume":"34","author":"M Hochbruck","year":"1997","unstructured":"Hochbruck, M., Lubich, C.: On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34(5), 1911\u20131925 (1997)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"761_CR13","doi-asserted-by":"publisher","first-page":"1552","DOI":"10.1137\/S1064827595295337","volume":"19","author":"M Hochbruck","year":"1998","unstructured":"Hochbruck, M., Lubich, C., Selhofer, H.: Exponential integrators for large systems of differential equations. SIAM J. Sci. Comput. 19(5), 1552\u20131574 (1998)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"761_CR14","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1137\/040611434","volume":"43","author":"M Hochbruck","year":"2005","unstructured":"Hochbruck, M., Ostermann, A.: Explicit exponential Runge\u2013Kutta methods for semilinear parabolic problems. SIAM J. Numer. Anal. 43(3), 1069\u20131090 (2005)","journal-title":"SIAM J. Numer. Anal."},{"key":"761_CR15","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1017\/S0962492910000048","volume":"19","author":"M Hochbruck","year":"2012","unstructured":"Hochbruck, M., Ostermann, A.: Exponential integrators. Acta Numer. 19, 209\u2013286 (2012)","journal-title":"Acta Numer."},{"key":"761_CR16","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.cam.2012.09.038","volume":"241","author":"J Loffeld","year":"2013","unstructured":"Loffeld, J., Tokman, M.: Comparative performance of exponential, implicit, and explicit integrators for stiff systems of odes. J. Comput. Appl. Math. 241, 45\u201367 (2013)","journal-title":"J. Comput. Appl. Math."},{"key":"761_CR17","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1017\/cbo9780511617652.004","volume-title":"Predictability of Weather and Climate","author":"EN Lorenz","year":"1996","unstructured":"Lorenz, E.N.: Predictability\u2014a problem partly solved. In: Palmer, T., Hagedorn, R. (eds.) Predictability of Weather and Climate, pp. 40\u201358. Cambridge University Press (CUP), Cambridge (1996). \n                    https:\/\/doi.org\/10.1017\/cbo9780511617652.004"},{"issue":"1","key":"761_CR18","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.cam.2003.08.006","volume":"161","author":"YY Lu","year":"2003","unstructured":"Lu, Y.Y.: Computing a matrix function for exponential integrators. J. Comput. Appl. Math. 161(1), 203\u2013216 (2003)","journal-title":"J. Comput. Appl. Math."},{"key":"761_CR19","unstructured":"Minchev, B.V., Wright, W.: A review of exponential integrators for first order semi-linear problems. Technical report (2005)"},{"issue":"3","key":"761_CR20","doi-asserted-by":"publisher","first-page":"22:1","DOI":"10.1145\/2168773.2168781","volume":"38","author":"J Niesen","year":"2012","unstructured":"Niesen, J., Wright, W.M.: Algorithm 919: a krylov subspace algorithm for evaluating the $$\\varphi $$-functions appearing in exponential integrators. ACM Trans. Math. Softw. 38(3), 22:1\u201322:19 (2012). \n                    https:\/\/doi.org\/10.1145\/2168773.2168781","journal-title":"ACM Trans. Math. Softw."},{"key":"761_CR21","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1016\/j.jcp.2016.07.026","volume":"323","author":"G Rainwater","year":"2016","unstructured":"Rainwater, G., Tokman, M.: A new approach to constructing efficient stiffly accurate Epirk methods. J. Comput. Phys. 323, 283\u2013309 (2016). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2016.07.026","journal-title":"J. Comput. Phys."},{"key":"761_CR22","unstructured":"Roberts, S., Popov, A., Sandu, A.: ODE Test Problems. \n                    https:\/\/sibiu.cs.vt.edu\/ode-test-problems\/index.html\n                    \n                  . Accessed 16 Dec 2017"},{"key":"761_CR23","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y Saad","year":"2003","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia (2003)"},{"issue":"6","key":"761_CR24","first-page":"561","volume":"60","author":"JC Schulze","year":"2008","unstructured":"Schulze, J.C., Schmid, P.J., Sesterhenn, J.L.: Exponential time integration using Krylov subspaces. Int. J. Numer. Meth. Fluids 60(6), 561\u2013609 (2008)","journal-title":"Int. J. Numer. Meth. Fluids"},{"issue":"1","key":"761_CR25","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1145\/285861.285868","volume":"24","author":"RB Sidje","year":"1998","unstructured":"Sidje, R.B.: Expokit: a software package for computing matrix exponentials. ACM Trans. Math. Softw. 24(1), 130\u2013156 (1998). \n                    https:\/\/doi.org\/10.1145\/285861.285868","journal-title":"ACM Trans. Math. Softw."},{"issue":"146","key":"761_CR26","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1090\/S0025-5718-1979-0521273-8","volume":"33","author":"T Steihaug","year":"1979","unstructured":"Steihaug, T., Wolfbrandt, A.: An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations. Math. Comput. 33(146), 521\u2013521 (1979). \n                    https:\/\/doi.org\/10.1090\/s0025-5718-1979-0521273-8","journal-title":"Math. Comput."},{"issue":"2","key":"761_CR27","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1016\/j.jcp.2005.08.032","volume":"213","author":"M Tokman","year":"2006","unstructured":"Tokman, M.: Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods. J. Comput. Phys. 213(2), 748\u2013776 (2006)","journal-title":"J. Comput. Phys."},{"key":"761_CR28","doi-asserted-by":"publisher","first-page":"8762","DOI":"10.1016\/j.jcp.2011.08.023","volume":"230","author":"M Tokman","year":"2011","unstructured":"Tokman, M.: A new class of exponential propagation iterative methods of Runge\u2013Kutta type (EPIRK). J. Comput. Phys. 230, 8762\u20138778 (2011)","journal-title":"J. Comput. Phys."},{"issue":"5","key":"761_CR29","doi-asserted-by":"publisher","first-page":"A2650","DOI":"10.1137\/110849961","volume":"34","author":"M Tokman","year":"2012","unstructured":"Tokman, M., Loffeld, J., Tranquilli, P.: New adaptive exponential propagation iterative methods of Runge\u2013Kutta type. SIAM J. Sci. Comput. 34(5), A2650\u2013A2669 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"761_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2016.05.002","author":"P Tranquilli","year":"2016","unstructured":"Tranquilli, P., Glandon, S.R., Sarshar, A., Sandu, A.: Analytical Jacobian-vector products for the matrix-free time integration of partial differential equations. J. Comput. Appl. Math. (2016). \n                    https:\/\/doi.org\/10.1016\/j.cam.2016.05.002","journal-title":"J. Comput. Appl. Math."},{"key":"761_CR31","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.jcp.2014.08.013","volume":"278","author":"P Tranquilli","year":"2014","unstructured":"Tranquilli, P., Sandu, A.: Exponential\u2013Krylov methods for ordinary differential equations. J. Comput. Phys. 278, 31\u201346 (2014). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2014.08.013","journal-title":"J. Comput. Phys."},{"issue":"3","key":"761_CR32","doi-asserted-by":"publisher","first-page":"A1313","DOI":"10.1137\/130923336","volume":"36","author":"P Tranquilli","year":"2014","unstructured":"Tranquilli, P., Sandu, A.: Rosenbrock\u2013Krylov methods for large systems of differential equations. SIAM J. Sci. Comput. 36(3), A1313\u2013A1338 (2014). \n                    https:\/\/doi.org\/10.1137\/130923336","journal-title":"SIAM J. Sci. Comput."},{"key":"761_CR33","first-page":"1","volume":"29","author":"LN Trefethen","year":"2007","unstructured":"Trefethen, L.N.: Evaluating matrix functions for exponential integrators via Carath\u00e9odory\u2013Fej\u00e9r approximation and contour integrals. Electron. Trans. Numer. Anal. 29, 1\u201318 (2007)","journal-title":"Electron. Trans. Numer. Anal."},{"issue":"4","key":"761_CR34","doi-asserted-by":"publisher","first-page":"1456","DOI":"10.1137\/S1064827597326651","volume":"20","author":"JG Verwer","year":"1999","unstructured":"Verwer, J.G., Spee, E.J., Blom, J.G., Hundsdorfer, W.: A second-order rosenbrock method applied to photochemical dispersion problems. SIAM J. Sci. Comput. 20(4), 1456\u20131480 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"761_CR35","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511615115","volume-title":"Iterative Krylov Methods for Large Linear Systems","author":"HA van der Vorst","year":"2003","unstructured":"van der Vorst, H.A.: Iterative Krylov Methods for Large Linear Systems. Cambridge University Press, Cambridge (2003). \n                    https:\/\/doi.org\/10.1017\/cbo9780511615115"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-018-0761-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0761-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0761-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T09:34:51Z","timestamp":1589708091000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-018-0761-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,14]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["761"],"URL":"https:\/\/doi.org\/10.1007\/s10915-018-0761-3","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,14]]},"assertion":[{"value":"20 February 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 December 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 June 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}