{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T00:34:41Z","timestamp":1726014881149},"publisher-location":"Cham","reference-count":15,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030115388"},{"type":"electronic","value":"9783030115395"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-11539-5_4","type":"book-chapter","created":{"date-parts":[[2019,3,8]],"date-time":"2019-03-08T15:26:23Z","timestamp":1552058783000},"page":"35-47","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Iterative Semi-implicit Splitting Methods for Stochastic Chemical Kinetics"],"prefix":"10.1007","author":[{"given":"J\u00fcrgen","family":"Geiser","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,1,26]]},"reference":[{"key":"4_CR1","unstructured":"Burkholder, D.L., Davis, B., Gundy, R.F.: Integral inequalities for convex functions of operators on martingales. In: Proceedings of 6th Berkeley Symposium on Mathematical Statistics and Probability, vol. 2, pp. 223\u2013240 (1972)"},{"issue":"9","key":"4_CR2","doi-asserted-by":"publisher","first-page":"4059","DOI":"10.1063\/1.1778376","volume":"121","author":"Y Cao","year":"2004","unstructured":"Cao, Y., Li, H., Petzold, L.: Efficient formulation of the stochastic simulation algorithm for chemically reacting systems. J. Chem. Phys. 121(9), 4059\u20134067 (2004)","journal-title":"J. Chem. Phys."},{"key":"4_CR3","doi-asserted-by":"crossref","first-page":"4992","DOI":"10.1016\/j.amc.2012.11.055","volume":"219","author":"Z Fan","year":"2013","unstructured":"Fan, Z.: SOR waveform relaxation methods for stochastic differential equations. Appl. Math. Comput. 219, 4992\u20135003 (2013)","journal-title":"Appl. Math. Comput."},{"key":"4_CR4","doi-asserted-by":"publisher","DOI":"10.1201\/b10947","volume-title":"Iterative Splitting Methods for Differential Equations, Numerical Analysis and Scientific Computing Series","author":"J Geiser","year":"2011","unstructured":"Geiser, J.: Iterative Splitting Methods for Differential Equations, Numerical Analysis and Scientific Computing Series. CRC Press, Chapman & Hall\/CRC, Boca Raton (2011). Edited by Magoules and Lai"},{"key":"4_CR5","doi-asserted-by":"crossref","unstructured":"Geiser, J.: Computing exponential for iterative splitting methods. J. Appl. Math. 2011, Article ID 193781 (2011)","DOI":"10.1155\/2011\/193781"},{"key":"4_CR6","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1166\/jcsmd.2013.1017","volume":"1","author":"J Geiser","year":"2013","unstructured":"Geiser, J.: Multiscale splitting for stochastic differential equations: applications in particle collisions. J. Coupled Syst. Multiscale Dyn. 1, 241\u2013250 (2013)","journal-title":"J. Coupled Syst. Multiscale Dyn."},{"issue":"4","key":"4_CR7","doi-asserted-by":"publisher","first-page":"1716","DOI":"10.1063\/1.1378322","volume":"115","author":"DT Gillespie","year":"2001","unstructured":"Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115(4), 1716\u20131733 (2001)","journal-title":"J. Chem. Phys."},{"issue":"7","key":"4_CR8","doi-asserted-by":"publisher","first-page":"2059","DOI":"10.1090\/S0002-9939-99-04801-7","volume":"127","author":"A Izzo","year":"1999","unstructured":"Izzo, A.: $$C^r$$ convergence of Picard\u2019s sucessive approximations. Proc. Am. Math. Soc. 127(7), 2059\u20132063 (1999)","journal-title":"Proc. Am. Math. Soc."},{"key":"4_CR9","series-title":"SIAM Frontiers in Applied Mathematics","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970944","volume-title":"Iterative Methods for Linear and Nonlinear Equations","author":"CT Kelley","year":"1995","unstructured":"Kelley, C.T.: Iterative Methods for Linear and Nonlinear Equations. SIAM Frontiers in Applied Mathematics, vol. 16. SIAM, Philadelphia (1995)"},{"key":"4_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12616-5","volume-title":"The Numerical Solution of Stochastic Differential Equations","author":"PE Kloeden","year":"1992","unstructured":"Kloeden, P.E., Platen, E.: The Numerical Solution of Stochastic Differential Equations. Springer, Heidelberg (1992). https:\/\/doi.org\/10.1007\/978-3-662-12616-5"},{"key":"4_CR11","first-page":"265","volume":"71","author":"B Kafash","year":"2014","unstructured":"Kafash, B., Lalehzari, R., Delavarkhalafi, A., Mahmoudi, E.: Application of stochastic differential system in chemical reactions via simulation. MATCH Commun. Math. Comput. Chem. 71, 265\u2013277 (2014)","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"4_CR12","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.spl.2017.05.016","volume":"129","author":"Z Li","year":"2017","unstructured":"Li, Z., Liu, J.: $$C^{\\infty }$$ -convergence of Picard\u2019s successive approximations to solutions of stochastic differential equations. Stat. Probab. Lett. 129, 203\u2013209 (2017)","journal-title":"Stat. Probab. Lett."},{"key":"4_CR13","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1017\/S096249290000266X","volume":"5","author":"U Miekkala","year":"1996","unstructured":"Miekkala, U., Nevanlinna, O.: Iterative solution of systems of linear differential equations. Acta Numerica 5, 259\u2013307 (1996)","journal-title":"Acta Numerica"},{"key":"4_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14394-6","volume-title":"Stochastic Differential Equations","author":"B Oksendal","year":"2003","unstructured":"Oksendal, B.: Stochastic Differential Equations. Springer, Berlin (2003). https:\/\/doi.org\/10.1007\/978-3-642-14394-6"},{"issue":"9","key":"4_CR15","first-page":"1232","volume":"38","author":"L Silva-Dias","year":"2015","unstructured":"Silva-Dias, L., Lopez-Castillo, A.: Practical stochastic model for chemical kintetics. Quim. Nova 38(9), 1232\u20131236 (2015)","journal-title":"Quim. Nova"}],"container-title":["Lecture Notes in Computer Science","Finite Difference Methods. Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-11539-5_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T14:18:54Z","timestamp":1663078734000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-11539-5_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030115388","9783030115395"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-11539-5_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"26 January 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FDM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Finite Difference Methods","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Lozenetz","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Bulgaria","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 June 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 June 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"fdm2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/parallel.bas.bg\/dpa\/FDM2018\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}