{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T19:46:57Z","timestamp":1743104817102,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":14,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662438794"},{"type":"electronic","value":"9783662438800"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-662-43880-0_69","type":"book-chapter","created":{"date-parts":[[2014,6,25]],"date-time":"2014-06-25T09:42:01Z","timestamp":1403689321000},"page":"602-610","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Splitting Numerical Scheme for Non-linear Models of Mathematical Finance"],"prefix":"10.1007","author":[{"given":"Miglena N.","family":"Koleva","sequence":"first","affiliation":[]},{"given":"Lubin G.","family":"Vulkov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,6,26]]},"reference":[{"key":"69_CR1","doi-asserted-by":"publisher","first-page":"1429","DOI":"10.1016\/j.nonrwa.2010.10.003","volume":"12","author":"R Agliardi","year":"2011","unstructured":"Agliardi, R., Popivanov, P., Slavova, A.: Nonhypoellipticity and comparison principle for partial differential equations of Black-Scholes type. Nonlinear Anal. Real Word Appl. 12, 1429\u20131436 (2011)","journal-title":"Nonlinear Anal. Real Word Appl."},{"key":"69_CR2","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1016\/j.camwa.2008.02.010","volume":"56","author":"R Company","year":"2008","unstructured":"Company, R., Navarro, E., Pintos, J., Ponsoda, E.: Numerical solution of linear and nonlinear Black-Scholes option pricing equations. Int. J. Comp. Math. Appl. 56, 813\u2013821 (2008)","journal-title":"Int. J. Comp. Math. Appl."},{"volume-title":"Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing","year":"2008","key":"69_CR3","unstructured":"Ehrhardt, M. (ed.): Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing. Nova Science Publishers, New York (2008)"},{"issue":"2","key":"69_CR4","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1002\/1098-2426(200103)17:2<152::AID-NUM5>3.0.CO;2-A","volume":"17","author":"A Gerisch","year":"2001","unstructured":"Gerisch, A., Griffiths, D.F., Weiner, R., Chaplain, M.A.J.: A positive splitting method for mixed hyperbolic-parabolic systems. Numer. Meth. PDEs 17(2), 152\u2013168 (2001)","journal-title":"Numer. Meth. PDEs"},{"key":"69_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-09017-6","volume-title":"Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations","author":"W Hundsdorfer","year":"2003","unstructured":"Hundsdorfer, W., Verwer, J.: Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Springer, Heidelberg (2003)"},{"key":"69_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/978-3-642-41515-9_40","volume-title":"Numerical Analysis and Its Applications","author":"MN Koleva","year":"2013","unstructured":"Koleva, M.N.: Positivity preserving numerical method for non-linear Black-Scholes models. In: Dimov, I., Farag\u00f3, I., Vulkov, L. (eds.) NAA 2012. LNCS, vol. 8236, pp. 363\u2013370. Springer, Heidelberg (2013)"},{"key":"69_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1007\/978-3-642-18466-6_55","volume-title":"Numerical Methods and Applications","author":"MN Koleva","year":"2011","unstructured":"Koleva, M.N., Vulkov, L.G.: A numerical study of a parabolic Monge-Amp\u00e8re equation in mathematical finance. In: Dimov, I., Dimova, S., Kolkovska, N. (eds.) NMA 2010. LNCS, vol. 6046, pp. 461\u2013468. Springer, Heidelberg (2011)"},{"issue":"9\u201310","key":"69_CR8","doi-asserted-by":"publisher","first-page":"2564","DOI":"10.1016\/j.mcm.2013.01.008","volume":"57","author":"M Koleva","year":"2013","unstructured":"Koleva, M., Vulkov, L.: Quasilinearization numerical scheme for fully nonlinear parabolic problems with applications in models of mathematical finance. Math. Comput. Model. 57(9\u201310), 2564\u20132575 (2013)","journal-title":"Math. Comput. Model."},{"key":"69_CR9","doi-asserted-by":"publisher","first-page":"885","DOI":"10.1016\/j.camwa.2004.03.014","volume":"49","author":"C-H Lai","year":"2005","unstructured":"Lai, C.-H., Parrott, A.K., Rout, S.: A distributed algorithm for European options with nonlinear volatility. Comput. Math. Appl. 49, 885\u2013894 (2005)","journal-title":"Comput. Math. Appl."},{"key":"69_CR10","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.cam.2007.02.035","volume":"214","author":"A-Y Le Roux","year":"2008","unstructured":"Le Roux, A.-Y., Le Roux, M.-N.: Numerical solution of a Cauchy problem for nonlinear reaction process. J. Comput. Appl. Math. 214, 90\u2013110 (2008)","journal-title":"J. Comput. Appl. Math."},{"key":"69_CR11","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1016\/j.apnum.2012.02.004","volume":"62","author":"M-N Le Roux","year":"2012","unstructured":"Le Roux, M.-N.: Numerical solution of a parabolic problem arising in finance. Appl. Numer. Math. 62, 815\u2013832 (2012)","journal-title":"Appl. Numer. Math."},{"key":"69_CR12","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.na.2005.05.047","volume":"65","author":"L Songzhe","year":"2006","unstructured":"Songzhe, L.: Existence of solution to initial value problem for a parabolic Monge-Amp\u00e8re equation and application. Nonlinear Anal. 65, 59\u201378 (2006)","journal-title":"Nonlinear Anal."},{"key":"69_CR13","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511812545","volume-title":"The Mathematics of Financial Derivatives: A Student Introduction","author":"P Wilmott","year":"1995","unstructured":"Wilmott, P., Howison, S., Dewynne, J.: The Mathematics of Financial Derivatives: A Student Introduction. Cambridge University Press, Cambridge (1995)"},{"key":"69_CR14","volume-title":"Mathematical Finance-Theory and Applications","author":"J Yong","year":"2000","unstructured":"Yong, J.: Introduction to mathematical finance. In: Yong, J., Cont, R. (eds.) Mathematical Finance-Theory and Applications. High Education Press, Beijing (2000)"}],"container-title":["Lecture Notes in Computer Science","Large-Scale Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-43880-0_69","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T19:39:11Z","timestamp":1674157151000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-662-43880-0_69"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783662438794","9783662438800"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-43880-0_69","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]},"assertion":[{"value":"26 June 2014","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}