{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:22:50Z","timestamp":1759191770033,"version":"3.37.3"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,6,7]],"date-time":"2020-06-07T00:00:00Z","timestamp":1591488000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,7]],"date-time":"2020-06-07T00:00:00Z","timestamp":1591488000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100002157","name":"Istituto Nazionale di Alta Matematica \u201cFrancesco Severi\u201d","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100002157","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e1 e della Ricerca","award":["PRIN2017"],"award-info":[{"award-number":["PRIN2017"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s40314-020-01200-z","type":"journal-article","created":{"date-parts":[[2020,6,7]],"date-time":"2020-06-07T05:02:18Z","timestamp":1591506138000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Jacobian-dependent vs Jacobian-free discretizations for nonlinear differential problems"],"prefix":"10.1007","volume":"39","author":[{"given":"Dajana","family":"Conte","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raffaele","family":"D\u2019Ambrosio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giovanni","family":"Pagano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Beatrice","family":"Paternoster","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,7]]},"reference":[{"issue":"1","key":"1200_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s002110100292","volume":"90","author":"A Abdulle","year":"2001","unstructured":"Abdulle A, Medovikov AA (2001) Second order Chebyshev methods based on orthogonal polynomials. Numer Math 90(1):1\u201318","journal-title":"Numer Math"},{"issue":"2","key":"1200_CR2","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1007\/s10915-018-0737-3","volume":"77","author":"P Bocher","year":"2018","unstructured":"Bocher P, Montijano JI, R\u00e1ndez L, Van Daele M (2018) Explicit Runge\u2013Kutta methods for stiff problems with a gap in their eigenvalue spectrum. J Sci Comput 77(2):1055\u20131083","journal-title":"J Sci Comput"},{"key":"1200_CR3","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.apnum.2017.02.004","volume":"116","author":"K Burrage","year":"2017","unstructured":"Burrage K, Cardone A, D\u2019Ambrosio R, Paternoster B (2017) Numerical solution of time fractional diffusion systems. Appl Numer Math 116:82\u201394","journal-title":"Appl Numer Math"},{"key":"1200_CR4","doi-asserted-by":"crossref","DOI":"10.1002\/9781119121534","volume-title":"Numerical methods for ordinary differential equations","author":"JC Butcher","year":"2016","unstructured":"Butcher JC (2016) Numerical methods for ordinary differential equations, 3rd edn. Wiley, Chichester","edition":"3"},{"key":"1200_CR5","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1063\/1.3241469","volume":"1168","author":"A Cardone","year":"2009","unstructured":"Cardone A, Conte D, Paternoster B (2009) A family of multistep collocation methods for volterra integro-differential equations. AIP Conf Proc 1168:358\u2013361","journal-title":"AIP Conf Proc"},{"key":"1200_CR6","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.cam.2016.08.025","volume":"316","author":"A Cardone","year":"2017","unstructured":"Cardone A, D\u2019Ambrosio R, Paternoster B (2017) Exponentially fitted IMEX methods for advection\u2013diffusion problems. J Comput Appl Math 316:100\u2013108","journal-title":"J Comput Appl Math"},{"key":"1200_CR7","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.apnum.2016.05.003","volume":"114C","author":"A Cardone","year":"2017","unstructured":"Cardone A, D\u2019Ambrosio R, Paternoster B (2017) High order exponentially fitted methods for Volterra integral equations with periodic solution. Appl Numer Math 114C:18\u201329","journal-title":"Appl Numer Math"},{"issue":"7","key":"1200_CR8","first-page":"2709","volume":"23","author":"A Cardone","year":"2018","unstructured":"Cardone A, Conte D, Paternoster B (2018) Two-step collocation methods for fractional differential equations. Discr Cont Dyn Syst B 23(7):2709\u20132725","journal-title":"Discr Cont Dyn Syst B"},{"key":"1200_CR9","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.apnum.2019.01.009","volume":"139","author":"A Cardone","year":"2019","unstructured":"Cardone A, D\u2019Ambrosio R, Paternoster B (2019) A spectral method for stochastic fractional differential equations. Appl Numer Math 139:115\u2013119","journal-title":"Appl Numer Math"},{"key":"1200_CR10","doi-asserted-by":"crossref","unstructured":"Chen C, Cohen D, D\u2019Ambrosio R, Lang A (2020) Drift-preserving numerical integrators for stochastic Hamiltonian systems. Adv Comput Math 46(2):27","DOI":"10.1007\/s10444-020-09771-5"},{"key":"1200_CR11","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.apnum.2019.08.011","volume":"150","author":"V Citro","year":"2020","unstructured":"Citro V, D\u2019Ambrosio R (2020) Long-term analysis of stochastic $$\\theta $$-methods for damped stochastic oscillators. Appl Numer Math 150:18\u201326","journal-title":"Appl Numer Math"},{"key":"1200_CR12","doi-asserted-by":"crossref","first-page":"106098","DOI":"10.1016\/j.aml.2019.106098","volume":"102","author":"V Citro","year":"2020","unstructured":"Citro V, D\u2019Ambrosio R, Di Giovacchino S (2020) A-stability preserving perturbation of Runge\u2013Kutta methods for stochastic differential equations. Appl Math Lett 102:106098","journal-title":"Appl Math Lett"},{"key":"1200_CR13","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.apnum.2018.01.002","volume":"127","author":"D Conte","year":"2018","unstructured":"Conte D, Califano G (2018) Optimal Schwarz Waveform Relaxation for fractional diffusion-wave equations. Appl Numer Math 127:125\u2013141","journal-title":"Appl Numer Math"},{"issue":"1","key":"1200_CR14","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s10915-016-0190-0","volume":"69","author":"D Conte","year":"2016","unstructured":"Conte D, Paternoster B (2016) Modified Gauss\u2013Laguerre exponential fitting based formulae. J Sci Comput 69(1):227\u2013243","journal-title":"J Sci Comput"},{"key":"1200_CR15","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.cpc.2009.08.007","volume":"181","author":"D Conte","year":"2010","unstructured":"Conte D, Esposito E, Gr L, Ixaru B (2010) Paternoster, Some new uses of the $$\\eta _m(Z)$$ functions. Comput Phys Commun 181:128\u2013137","journal-title":"Comput Phys Commun"},{"issue":"1","key":"1200_CR16","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.cam.2012.08.012","volume":"239","author":"D Conte","year":"2013","unstructured":"Conte D, D\u2019Ambrosio R, Jackiewicz Z, Paternoster B (2013) Numerical search for algebraically stable two-step almost collocation methods. J Comput Appl Math 239(1):304\u2013321","journal-title":"J Comput Appl Math"},{"key":"1200_CR17","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1016\/j.cam.2013.06.040","volume":"255","author":"D Conte","year":"2014","unstructured":"Conte D, Ixaru L, Gr L, Paternoster B, Santomauro G (2014) Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval. J Comput Appl Math 255:725\u2013736","journal-title":"J Comput Appl Math"},{"issue":"2","key":"1200_CR18","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s11075-015-9993-6","volume":"71","author":"D Conte","year":"2016","unstructured":"Conte D, D\u2019Ambrosio R, Paternoster B (2016) GPU acceleration of waveform relaxation methods for large differential systems. Numer Algor 71(2):293\u2013310","journal-title":"Numer Algor"},{"key":"1200_CR19","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.apnum.2017.02.008","volume":"119","author":"D Conte","year":"2017","unstructured":"Conte D, Capobianco G, Paternoster B (2017) Construction and implementation of two-step continuous methods for Volterra Integral Equations. Appl Numer Math 119:239\u2013247","journal-title":"Appl Numer Math"},{"issue":"7","key":"1200_CR20","first-page":"2695","volume":"23","author":"D Conte","year":"2018","unstructured":"Conte D, D\u2019Ambrosio R, Paternoster B (2018) On the stability of $$\\vartheta $$-methods for stochastic Volterra integral equations. Discr Cont Dyn Syst Ser B 23(7):2695\u20132708","journal-title":"Discr Cont Dyn Syst Ser B"},{"key":"1200_CR21","doi-asserted-by":"crossref","unstructured":"Conte D, D\u2019Ambrosio R, Moccaldi M, Paternoster B (2019) Adapted explicit two-step peer methods. J Numer Math 27(2):69\u201383","DOI":"10.1515\/jnma-2017-0102"},{"key":"1200_CR22","doi-asserted-by":"publisher","unstructured":"Conte D, Mohammadi F, Moradi L, Paternoster B (2020) Exponentially fitted two-step peer methods for oscillatory problems. Comput Appl Math. https:\/\/doi.org\/10.1007\/s40314-020-01202-x","DOI":"10.1007\/s40314-020-01202-x"},{"issue":"3","key":"1200_CR23","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1007\/s10915-013-9812-y","volume":"60","author":"R D\u2019Ambrosio","year":"2014","unstructured":"D\u2019Ambrosio R, Hairer E (2014) Long-term stability of multi-value methods for ordinary differential equations. J Sci Comput 60(3):627\u2013640","journal-title":"J Sci Comput"},{"issue":"1","key":"1200_CR24","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1186\/2193-1801-3-425","volume":"3","author":"R D\u2019Ambrosio","year":"2014","unstructured":"D\u2019Ambrosio R, Paternoster B (2014) Numerical solution of a diffusion problem by exponentially fitted finite difference methods. SpringerPlus 3(1):425\u2013431","journal-title":"SpringerPlus"},{"key":"1200_CR25","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/j.cam.2013.12.022","volume":"263","author":"R D\u2019Ambrosio","year":"2014","unstructured":"D\u2019Ambrosio R, Paternoster B (2014) Exponentially fitted singly diagonally implicit Runge\u2013Kutta methods. J Comput Appl Math 263:277\u2013287","journal-title":"J Comput Appl Math"},{"issue":"1","key":"1200_CR26","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.matcom.2014.04.007","volume":"110","author":"R D\u2019Ambrosio","year":"2015","unstructured":"D\u2019Ambrosio R, Paternoster B (2015) A general framework for numerical methods solving second order differential problems. Math Comput Simul 110(1):113\u2013124","journal-title":"Math Comput Simul"},{"key":"1200_CR27","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1016\/j.cam.2015.08.012","volume":"294","author":"R D\u2019Ambrosio","year":"2016","unstructured":"D\u2019Ambrosio R, Paternoster B (2016) Numerical solution of reaction\u2013diffusion systems of $$\\lambda -\\omega $$ type by trigonometrically fitted methods. J Comput Appl Math 294:436\u2013445","journal-title":"J Comput Appl Math"},{"key":"1200_CR28","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.cpc.2010.10.009","volume":"182","author":"R D\u2019Ambrosio","year":"2011","unstructured":"D\u2019Ambrosio R, Gr L, Ixaru L, Paternoster B (2011) Construction of the EF-based Runge-Kutta methods revisited. Comput Phys Commun 182:322\u2013329","journal-title":"Comput Phys Commun"},{"issue":"2","key":"1200_CR29","first-page":"553","volume":"40","author":"R D\u2019Ambrosio","year":"2014","unstructured":"D\u2019Ambrosio R, De Martino G, Paternoster B (2014) Numerical integration of Hamiltonian problems by G-symplectic methods. Adv Comput Math 40(2):553\u2013575","journal-title":"Adv Comput Math"},{"issue":"3","key":"1200_CR30","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/s11075-013-9819-3","volume":"65","author":"R D\u2019Ambrosio","year":"2014","unstructured":"D\u2019Ambrosio R, De Martino G, Paternoster B (2014) Order conditions of general Nystr\u00f6m methods. Numer.Algor 65(3):579\u2013595","journal-title":"Numer.Algor"},{"key":"1200_CR31","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.aml.2013.10.013","volume":"30","author":"R D\u2019Ambrosio","year":"2014","unstructured":"D\u2019Ambrosio R, Paternoster B, Santomauro G (2014) Revised exponentially fitted Runge\u2013Kutta\u2013Nystr\u00f6m methods. Appl Math Lett 30:56\u201360","journal-title":"Appl Math Lett"},{"issue":"5","key":"1200_CR32","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1016\/j.camwa.2017.04.023","volume":"74","author":"R D\u2019Ambrosio","year":"2017","unstructured":"D\u2019Ambrosio R, Moccaldi M, Paternoster B (2017) Adapted numerical methods for advection\u2013reaction\u2013diffusion problems generating periodic wavefronts. Comput Appl Math 74(5):1029\u20131042","journal-title":"Comput Appl Math"},{"issue":"10","key":"1200_CR33","doi-asserted-by":"crossref","first-page":"2867","DOI":"10.1007\/s10910-018-0922-5","volume":"56","author":"R D\u2019Ambrosio","year":"2018","unstructured":"D\u2019Ambrosio R, Moccaldi M, Paternoster B, Rossi F (2018) Adapted numerical modelling of the Belousov\u2013Zhabotinsky reaction. J Math Chem 56(10):2867\u20132897","journal-title":"J Math Chem"},{"key":"1200_CR34","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.cpc.2018.01.007","volume":"226","author":"R D\u2019Ambrosio","year":"2018","unstructured":"D\u2019Ambrosio R, Moccaldi M, Paternoster B (2018) Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems. Comp Phys Commun 226:55\u201366","journal-title":"Comp Phys Commun"},{"issue":"7","key":"1200_CR35","first-page":"2763","volume":"23","author":"R D\u2019Ambrosio","year":"2018","unstructured":"D\u2019Ambrosio R, Moccaldi M, Paternoster B (2018) Numerical preservation of long-term dynamics by stochastic two-step methods. Discr Cont Dyn Syst Ser B 23(7):2763\u20132773","journal-title":"Discr Cont Dyn Syst Ser B"},{"key":"1200_CR36","volume-title":"Solving ordinary differential equations ii\u2014stiff and differential\u2014algebraic problems","author":"E Hairer","year":"2002","unstructured":"Hairer E, Wanner G (2002) Solving ordinary differential equations ii\u2014stiff and differential\u2014algebraic problems. Springer, Berlin"},{"key":"1200_CR37","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12607-3","volume-title":"Solving ordinary differential equations I. Non-stiff problems","author":"E Hairer","year":"1987","unstructured":"Hairer E, N\u00f8rsett S, Wanner G (1987) Solving ordinary differential equations I. Non-stiff problems. Springer, Berlin"},{"key":"1200_CR38","volume-title":"Analysis of numerical methods","author":"E Isaacson","year":"1994","unstructured":"Isaacson E, Keller HB (1994) Analysis of numerical methods. Dover Publications, New York"},{"key":"1200_CR39","doi-asserted-by":"crossref","unstructured":"Ixaru L Gr (2012) Runge\u2013Kutta method with equation dependent coefficients. Comput Phys Commun 183(1):63\u201369","DOI":"10.1016\/j.cpc.2011.08.017"},{"key":"1200_CR40","doi-asserted-by":"crossref","unstructured":"Ixaru L Gr (2013) Runge\u2013Kutta methods with equation dependent coefficients. Lect Notes Comput Sci 8236:327\u2013336","DOI":"10.1007\/978-3-642-41515-9_36"},{"key":"1200_CR41","doi-asserted-by":"crossref","unstructured":"Ixaru L Gr (2013) Runge\u2013Kutta methods of special form. J Phys Conf Ser 413(1) Article number 012033","DOI":"10.1088\/1742-6596\/413\/1\/012033"},{"key":"1200_CR42","doi-asserted-by":"crossref","unstructured":"Ixaru L Gr (2019) Exponential and trigonometrical fittings: user-friendly expressions for the coefficients. Numer Algorithms 82:1085\u20131096","DOI":"10.1007\/s11075-018-0642-8"},{"key":"1200_CR43","doi-asserted-by":"crossref","unstructured":"Ixaru L Gr, Vanden Berghe G (2004) Exponential Fitting. Kluwer, Boston, Dordrecht, London","DOI":"10.1007\/978-1-4020-2100-8"},{"issue":"10","key":"1200_CR44","doi-asserted-by":"crossref","first-page":"1802","DOI":"10.1016\/j.cpc.2009.05.006","volume":"180","author":"J Mart\u00e1n-Vaquero","year":"2009","unstructured":"Mart\u00e1n-Vaquero J, Janssen B (2009) Second-order stabilized explicit Runge\u2013Kutta methods for stiff problems. Comput Phys Commun 180(10):1802\u20131810","journal-title":"Comput Phys Commun"},{"issue":"4","key":"1200_CR45","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s11075-008-9202-y","volume":"48","author":"J Mart\u00e1n-Vaquero","year":"2008","unstructured":"Mart\u00e1n-Vaquero J, Vigo-Aguiar J (2008) Exponential fitted Gauss, Radau and Lobatto methods of low order. Numer Algorithms 48(4):327\u2013346","journal-title":"Numer Algorithms"},{"issue":"1","key":"1200_CR46","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF03167357","volume":"18","author":"K Ozawa","year":"2001","unstructured":"Ozawa K (2001) A functional fitting Runge\u2013Kutta method with variable coefficients. Jpn J Ind Appl Math 18(1):107\u2013130","journal-title":"Jpn J Ind Appl Math"},{"key":"1200_CR47","doi-asserted-by":"crossref","first-page":"2499","DOI":"10.1016\/j.cpc.2012.06.013","volume":"183","author":"B Paternoster","year":"2012","unstructured":"Paternoster B (2012) Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70-th anniversary. Comput Phys Commun 183:2499\u20132512","journal-title":"Comput Phys Commun"},{"key":"1200_CR48","volume-title":"The numerical method of lines: integration of partial differential equations","author":"WE Schiesser","year":"1991","unstructured":"Schiesser WE (1991) The numerical method of lines: integration of partial differential equations. Academic Press, Cambridge"},{"key":"1200_CR49","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511576270","volume-title":"A compendium of partial differential equation models: method of lines analysis with matlab","author":"WE Schiesser","year":"2009","unstructured":"Schiesser WE, Griffiths GW (2009) A compendium of partial differential equation models: method of lines analysis with matlab. Cambridge University Press, Cambridge"},{"key":"1200_CR50","volume-title":"Numerical solution of partial differential equations\u2014finite difference methods","author":"GD Smith","year":"1985","unstructured":"Smith GD (1985) Numerical solution of partial differential equations\u2014finite difference methods. Clarendon Press, Oxford"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01200-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-020-01200-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01200-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,6]],"date-time":"2021-06-06T23:11:24Z","timestamp":1623021084000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-020-01200-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,7]]},"references-count":50,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["1200"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01200-z","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2020,6,7]]},"assertion":[{"value":"3 December 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 May 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 June 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"171"}}