{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:16:58Z","timestamp":1777454218705,"version":"3.51.4"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,9,9]],"date-time":"2017-09-09T00:00:00Z","timestamp":1504915200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2018,7]]},"DOI":"10.1007\/s11075-017-0408-8","type":"journal-article","created":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T18:18:37Z","timestamp":1505153917000},"page":"957-981","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["PDE-W-methods for parabolic problems with mixed derivatives"],"prefix":"10.1007","volume":"78","author":[{"given":"S.","family":"Gonz\u00e1lez-Pinto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"Hairer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"Hern\u00e1ndez-Abreu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"P\u00e9rez-Rodr\u00edguez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,9,9]]},"reference":[{"issue":"4","key":"408_CR1","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/0898-1221(88)90150-2","volume":"16","author":"IJD Craig","year":"1988","unstructured":"Craig, I.J.D., Sneyd, A.D.: An alternating-direction implicit scheme for parabolic equations with mixed derivatives. Comput. Math. Appl. 16(4), 341\u2013350 (1988)","journal-title":"Comput. Math. Appl."},{"key":"408_CR2","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1090\/S0002-9947-1956-0084194-4","volume":"82","author":"JJr Douglas","year":"1956","unstructured":"Douglas, J. Jr., Rachford, H.H. Jr.: On the numerical solution of heat conduction problems in two and three space variables. Trans. Amer. Math. Soc. 82, 421\u2013439 (1956)","journal-title":"Trans. Amer. Math. Soc."},{"key":"408_CR3","doi-asserted-by":"crossref","unstructured":"D\u00fcring, B., Fourni\u00e9, M., Rigal, A.: High-order ADI schemes for convection-diffusion equations with mixed derivative terms. In: Spectral and high order methods for partial differential equations\u2014ICOSAHOM 2012, vol. 95 of Lect. Notes Comput. Sci. Eng., pp 217\u2013226. Springer, Cham (2014)","DOI":"10.1007\/978-3-319-01601-6_17"},{"key":"408_CR4","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.cam.2016.09.040","volume":"316","author":"B D\u00fcring","year":"2017","unstructured":"D\u00fcring, B., Miles, J.: High-order ADI scheme for option pricing in stochastic volatility models. J. Comput. Appl. Math. 316, 109\u2013121 (2017)","journal-title":"J. Comput. Appl. Math."},{"issue":"1\u20133","key":"408_CR5","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/S0168-9274(01)00148-9","volume":"42","author":"A Gerisch","year":"2002","unstructured":"Gerisch, A., Verwer, J.G.: Operator splitting and approximate factorization for taxis-diffusion-reaction models. Appl. Numer. Math. 42(1\u20133), 159\u2013176 (2002). Ninth Seminar on Numerical Solution of Differential and Differential-Algebraic Equations (Halle, 2000)","journal-title":"Appl. Numer. Math."},{"key":"408_CR6","doi-asserted-by":"crossref","unstructured":"Hairer, E., Wanner, G.: Solving ordinary differential equations II. stiff and differential-algebraic problems. Springer Series in Computational Mathematics 14, 2nd edn. Springer, Berlin (1996)","DOI":"10.1007\/978-3-642-05221-7_1"},{"key":"408_CR7","first-page":"36","volume":"101","author":"C Hendricks","year":"2016","unstructured":"Hendricks, C., Ehrhardt, M., G\u00fcnther, M.: High-order ADI schemes for diffusion equations with mixed derivatives in the combination technique. Appl. Numer. Math. 101, 36\u201352 (2016)","journal-title":"Math."},{"key":"408_CR8","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.cam.2016.08.044","volume":"316","author":"C Hendricks","year":"2017","unstructured":"Hendricks, C., Heuer, C., Ehrhardt, M., G\u00fcnther, M.: High-order ADI finite difference schemes for parabolic equations in the combination technique with application in finance. J. Comput. Appl. Math. 316, 175\u2013194 (2017)","journal-title":"J. Comput. Appl. Math."},{"issue":"1\u20133","key":"408_CR9","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/S0168-9274(01)00152-0","volume":"42","author":"W Hundsdorfer","year":"2002","unstructured":"Hundsdorfer, W.: Accuracy and stability of splitting with stabilizing corrections. Appl. Numer. Math. 42(1\u20133), 213\u2013233 (2002). Ninth Seminar on Numerical Solution of Differential and Differential-Algebraic Equations (Halle, 2000)","journal-title":"Appl. Numer. Math."},{"key":"408_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-09017-6","volume-title":"Numerical solution of time-dependent advection-diffusion-reaction equations, volume 33 of Springer Series in Computational Mathematics","author":"W Hundsdorfer","year":"2003","unstructured":"Hundsdorfer, W., Verwer, J.G.: Numerical solution of time-dependent advection-diffusion-reaction equations, volume 33 of Springer Series in Computational Mathematics. Springer, Berlin (2003)"},{"issue":"3-4","key":"408_CR11","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1016\/j.apnum.2008.03.016","volume":"59","author":"KJ in \u2019t Hout","year":"2009","unstructured":"in \u2019t Hout, K.J., Welfert, B.D.: Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms. Appl. Numer. Math. 59(3-4), 677\u2013692 (2009)","journal-title":"Appl. Numer. Math."},{"key":"408_CR12","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.cam.2015.09.023","volume":"296","author":"KJ in \u2019t Hout","year":"2016","unstructured":"in \u2019t Hout, K.J., Wyns, M.: Convergence of the modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with mixed derivative term. J. Comput. Appl. Math. 296, 170\u2013180 (2016)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"408_CR13","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s00211-013-0516-x","volume":"124","author":"J Lang","year":"2013","unstructured":"Lang, J., Verwer, J.G.: W-methods in optimal control. Numer. Math. 124 (2), 337\u2013360 (2013)","journal-title":"Numer. Math."},{"key":"408_CR14","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1137\/0103003","volume":"3","author":"DW Peaceman","year":"1955","unstructured":"Peaceman, D.W., Rachford, H.H. Jr.: The numerical solution of parabolic and elliptic differential equations. J. Soc. Indust. Appl. Math. 3, 28\u201341 (1955)","journal-title":"J. Soc. Indust. Appl. Math."},{"key":"408_CR15","first-page":"565","volume":"274","author":"S Gonz\u00e1lez Pinto","year":"2016","unstructured":"Gonz\u00e1lez Pinto, S., Hern\u00e1ndez Abreu, D., P\u00e9rez Rodr\u00edguez, S., Weiner, R.: A family of three-stage third order AMF-w-methods for the time integration of advection diffusion reaction PDEs. Appl. Math. Comput. 274, 565\u2013584 (2016)","journal-title":"Appl. Math. Comput."},{"issue":"4","key":"408_CR16","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1007\/s10543-005-0035-y","volume":"45","author":"J Rang","year":"2005","unstructured":"Rang, J., Angermann, L.: New Rosenbrock W-methods of order 3 for partial differential algebraic equations of index 1. BIT 45(4), 761\u2013787 (2005)","journal-title":"BIT"},{"issue":"146","key":"408_CR17","doi-asserted-by":"crossref","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. Comp. 33 (146), 521\u2013534 (1979)","journal-title":"Math. Comp."},{"issue":"1\u20132","key":"408_CR18","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/S0377-0427(00)00523-9","volume":"128","author":"PJ Houwen van der","year":"2001","unstructured":"van der Houwen, P.J., Sommeijer, B.P.: Approximate factorization for time-dependent partial differential equations. J. Comput. Appl. Math. 128(1\u20132), 447\u2013466 (2001). Numerical analysis 2000, Vol. VII, Partial differential equations","journal-title":"J. Comput. Appl. Math."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-017-0408-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0408-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-017-0408-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,3]],"date-time":"2019-10-03T09:49:39Z","timestamp":1570096179000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-017-0408-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,9]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["408"],"URL":"https:\/\/doi.org\/10.1007\/s11075-017-0408-8","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,9]]}}}