{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:31:35Z","timestamp":1776846695562,"version":"3.51.2"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2010,2,5]],"date-time":"2010-02-05T00:00:00Z","timestamp":1265328000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2010,4]]},"DOI":"10.1007\/s10208-010-9061-5","type":"journal-article","created":{"date-parts":[[2010,2,4]],"date-time":"2010-02-04T16:09:55Z","timestamp":1265299795000},"page":"171-190","source":"Crossref","is-referenced-by-count":19,"title":["Convergence of a Time Discretisation for Doubly Nonlinear Evolution Equations of\u00a0Second\u00a0Order"],"prefix":"10.1007","volume":"10","author":[{"given":"Etienne","family":"Emmrich","sequence":"first","affiliation":[]},{"given":"Mechthild","family":"Thalhammer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,2,5]]},"reference":[{"key":"9061_CR1","first-page":"224","volume":"34","author":"G. Andreassi","year":"1964","unstructured":"G. Andreassi, G. Torelli, Si una equazione di tipo iperbolico non lineare, Rend. Sem. Mat. Univ. Padova 34, 224\u2013241 (1964).","journal-title":"Rend. Sem. Mat. Univ. Padova"},{"key":"9061_CR2","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1080\/00036818908839875","volume":"33","author":"D. Bahuguna","year":"1989","unstructured":"D. Bahuguna, Application of Rothe\u2019s method to semilinear hyperbolic equations, Appl. Anal. 33, 233\u2013242 (1989).","journal-title":"Appl. Anal."},{"key":"9061_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-010-1537-0","volume-title":"Nonlinear Semigroups and Differential Equations in Banach Spaces","author":"V. Barbu","year":"1976","unstructured":"V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces (Noordhoff, Leyden, 1976)."},{"issue":"3","key":"9061_CR4","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1155\/S0161171296000683","volume":"19","author":"P. Colli","year":"1996","unstructured":"P. Colli, A. Favini, Time discretization of nonlinear Cauchy problems applying to mixed hyperbolic-parabolic equations, Int. J. Math. Math. Sci. 19(3), 481\u2013494 (1996).","journal-title":"Int. J. Math. Math. Sci."},{"issue":"4","key":"9061_CR5","first-page":"827","volume":"6","author":"E. Emmrich","year":"2008","unstructured":"E. Emmrich, Two-step BDF time discretisation of nonlinear evolution problems governed by monotone operators with strongly continuous perturbations, Comput. Methods Appl. Math. 6(4), 827\u2013843 (2008).","journal-title":"Comput. Methods Appl. Math."},{"issue":"3","key":"9061_CR6","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s10092-009-0007-8","volume":"46","author":"E. Emmrich","year":"2009","unstructured":"E. Emmrich, Variable time-step \u03d1-scheme for nonlinear evolution equations governed by a monotone operator, Calcolo 46(3), 187\u2013210 (2009).","journal-title":"Calcolo"},{"key":"9061_CR7","doi-asserted-by":"crossref","unstructured":"E. Emmrich, M. Thalhammer, Stiffly accurate Runge\u2013Kutta methods for nonlinear evolution problems governed by a monotone operator, Math. Comput. Published on line first (DOI: 10.1090\/S0025-5718-09-02285-6 ).","DOI":"10.1090\/S0025-5718-09-02285-6"},{"key":"9061_CR8","series-title":"North-Holland Mathematics Studies","volume-title":"Second Order Linear Differential Equations in Banach Spaces","author":"H.O. Fattorini","year":"1985","unstructured":"H.O. Fattorini, Second Order Linear Differential Equations in Banach Spaces, North-Holland Mathematics Studies, vol. 108 (Elsevier, Amsterdam, 1985)."},{"issue":"1","key":"9061_CR9","doi-asserted-by":"crossref","first-page":"29","DOI":"10.2140\/pjm.1988.135.29","volume":"135","author":"A. Friedman","year":"1988","unstructured":"A. Friedman, J. Ne\u010das, Systems of nonlinear wave equations with nonlinear viscosity, Pac. J. Math. 135(1), 29\u201355 (1988).","journal-title":"Pac. J. Math."},{"key":"9061_CR10","doi-asserted-by":"crossref","DOI":"10.1515\/9783112717899","volume-title":"Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen","author":"H. Gajewski","year":"1974","unstructured":"H. Gajewski, K. Gr\u00f6ger, K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen (Akademie, Berlin, 1974)."},{"key":"9061_CR11","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/0022-247X(69)90257-1","volume":"25","author":"J.M. Greenberg","year":"1969","unstructured":"J.M. Greenberg, On the existence, uniqueness, and stability of solutions of the equation \u03c1 0 X tt =E(X x )X xx +\u03bb X xxt , J. Math. Anal. Appl. 25, 575\u2013591 (1969).","journal-title":"J. Math. Anal. Appl."},{"key":"9061_CR12","first-page":"707","volume":"17","author":"J.M. Greenberg","year":"1967\/1968","unstructured":"J.M. Greenberg, R.C. MacCamy, V.J. Mizel, On the existence, uniqueness, and stability of solutions of the equation \u03c3\u2032(u x )u xx +\u03bb u xtx =\u03c1 0 u tt , J. Math. Mech. 17, 707\u2013728 (1967\/1968).","journal-title":"J. Math. Mech."},{"key":"9061_CR13","volume-title":"Quelques M\u00e9thodes de R\u00e9solution des Probl\u00e8mes aux Limites Non Lin\u00e9aires","author":"J.-L. Lions","year":"1969","unstructured":"J.-L. Lions, Quelques M\u00e9thodes de R\u00e9solution des Probl\u00e8mes aux Limites Non Lin\u00e9aires (Dunod, Gauthier-Villars, Paris, 1969)."},{"key":"9061_CR14","first-page":"43","volume":"93","author":"J.-L. Lions","year":"1965","unstructured":"J.-L. Lions, W.A. Strauss, Some non-linear evolution equations, Bull. SMF 93, 43\u201396 (1965).","journal-title":"Bull. SMF"},{"key":"9061_CR15","volume-title":"Introduction \u00e0 l\u2019Analyse Num\u00e9rique des \u00c9quations aux D\u00e9riv\u00e9es Partielles","author":"P.A. Raviart","year":"1983","unstructured":"P.A. Raviart, J.M. Thomas, Introduction \u00e0 l\u2019Analyse Num\u00e9rique des \u00c9quations aux D\u00e9riv\u00e9es Partielles (Masson, Paris, 1983)."},{"key":"9061_CR16","volume-title":"Nonlinear Partial Differential Equations with Applications","author":"T. Roub\u00ed\u010dek","year":"2005","unstructured":"T. Roub\u00ed\u010dek, Nonlinear Partial Differential Equations with Applications (Birkh\u00e4user, Basel, 2005)."},{"issue":"1","key":"9061_CR17","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1007\/BF01990352","volume":"33","author":"R.D. Skeel","year":"1993","unstructured":"R.D. Skeel, Variable step size destabilizes the St\u00f6rmer\/leapfrog\/Verlet method, BIT 33(1), 172\u2013175 (1993).","journal-title":"BIT"},{"key":"9061_CR18","volume-title":"Nonlinear Functional Analysis and Its Applications, II\/B: Nonlinear Monotone Operators","author":"E. Zeidler","year":"1990","unstructured":"E. Zeidler, Nonlinear Functional Analysis and Its Applications, II\/B: Nonlinear Monotone Operators (Springer, New York, 1990)."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-010-9061-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-010-9061-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-010-9061-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T12:06:58Z","timestamp":1739794018000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-010-9061-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,2,5]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,4]]}},"alternative-id":["9061"],"URL":"https:\/\/doi.org\/10.1007\/s10208-010-9061-5","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,2,5]]}}}