{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:18Z","timestamp":1740123558764,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,3,3]],"date-time":"2018-03-03T00:00:00Z","timestamp":1520035200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100002790","name":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002790","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,9]]},"DOI":"10.1007\/s10915-018-0685-y","type":"journal-article","created":{"date-parts":[[2018,3,3]],"date-time":"2018-03-03T15:43:34Z","timestamp":1520091814000},"page":"1839-1867","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Monotone Mixed Finite Difference Scheme for Monge\u2013Amp\u00e8re Equation"],"prefix":"10.1007","volume":"76","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5101-7596","authenticated-orcid":false,"given":"Yangang","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Justin W. L.","family":"Wan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jessey","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,3]]},"reference":[{"issue":"3","key":"685_CR1","doi-asserted-by":"publisher","first-page":"1341","DOI":"10.1137\/15M1043431","volume":"54","author":"P Azimzadeh","year":"2016","unstructured":"Azimzadeh, P., Forsyth, P.A.: Weakly chained matrices, policy iteration, and impulse control. SIAM J. Numer. Anal. 54(3), 1341\u20131364 (2016). https:\/\/doi.org\/10.1137\/15M1043431","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"685_CR2","doi-asserted-by":"crossref","first-page":"271","DOI":"10.3233\/ASY-1991-4305","volume":"4","author":"G Barles","year":"1991","unstructured":"Barles, G., Souganidis, P.E.: Convergence of approximation schemes for fully nonlinear second order equations. Asymptot. Anal. 4(3), 271\u2013283 (1991)","journal-title":"Asymptot. Anal."},{"issue":"302","key":"685_CR3","doi-asserted-by":"publisher","first-page":"2743","DOI":"10.1090\/mcom\/3080","volume":"85","author":"JD Benamou","year":"2016","unstructured":"Benamou, J.D., Collino, F., Mirebeau, J.M.: Monotone and consistent discretization of the Monge\u2013Amp\u00e8re operator. Math. Comput. 85(302), 2743\u20132775 (2016). https:\/\/doi.org\/10.1090\/mcom\/3080","journal-title":"Math. Comput."},{"issue":"4","key":"685_CR4","doi-asserted-by":"publisher","first-page":"737","DOI":"10.1051\/m2an\/2010017","volume":"44","author":"JD Benamou","year":"2010","unstructured":"Benamou, J.D., Froese, B.D., Oberman, A.M.: Two numerical methods for the elliptic Monge\u2013Amp\u00e8re equation. M2AN. Math. Model. Numer. Anal. 44(4), 737\u2013758 (2010). https:\/\/doi.org\/10.1051\/m2an\/2010017","journal-title":"Math. Model. Numer. Anal."},{"issue":"3","key":"685_CR5","doi-asserted-by":"publisher","first-page":"1212","DOI":"10.1137\/040621740","volume":"46","author":"K B\u00f6hmer","year":"2008","unstructured":"B\u00f6hmer, K.: On finite element methods for fully nonlinear elliptic equations of second order. SIAM J. Numer. Anal. 46(3), 1212\u20131249 (2008). https:\/\/doi.org\/10.1137\/040621740","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"685_CR6","doi-asserted-by":"publisher","first-page":"3001","DOI":"10.1137\/08073041X","volume":"47","author":"O Bokanowski","year":"2009","unstructured":"Bokanowski, O., Maroso, S., Zidani, H.: Some convergence results for Howard\u2019s algorithm. SIAM J. Numer. Anal. 47(4), 3001\u20133026 (2009). https:\/\/doi.org\/10.1137\/08073041X","journal-title":"SIAM J. Numer. Anal."},{"issue":"276","key":"685_CR7","doi-asserted-by":"publisher","first-page":"1979","DOI":"10.1090\/S0025-5718-2011-02487-7","volume":"80","author":"SC Brenner","year":"2011","unstructured":"Brenner, S.C., Gudi, T., Neilan, M., Sung, Ly: $$C^0$$ C 0 penalty methods for the fully nonlinear Monge\u2013Amp\u00e8re equation. Math. Comput. 80(276), 1979\u20131995 (2011). https:\/\/doi.org\/10.1090\/S0025-5718-2011-02487-7","journal-title":"Math. Comput."},{"key":"685_CR8","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/226","volume-title":"Monge\u2013Amp\u00e8re equation: applications to geometry and optimization, Contemporary Mathematics","year":"1999","unstructured":"Caffarelli, L.A., Milman, M. (eds.): Monge\u2013Amp\u00e8re equation: applications to geometry and optimization, Contemporary Mathematics, vol. 226. American Mathematical Society, Providence (1999). https:\/\/doi.org\/10.1090\/conm\/226"},{"key":"685_CR9","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1007\/BF01844166","volume":"4","author":"PG Ciarlet","year":"1970","unstructured":"Ciarlet, P.G.: Discrete maximum principle for finite-difference operators. Aequ. Math. 4, 338\u2013352 (1970)","journal-title":"Aequ. Math."},{"issue":"1","key":"685_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0273-0979-1992-00266-5","volume":"27","author":"MG Crandall","year":"1992","unstructured":"Crandall, M.G., Ishii, H., Lions, P.L.: User\u2019s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. (N.S.) 27(1), 1\u201367 (1992). https:\/\/doi.org\/10.1090\/S0273-0979-1992-00266-5","journal-title":"Bull. Am. Math. Soc. (N.S.)"},{"issue":"1","key":"685_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1090\/S0002-9947-1983-0690039-8","volume":"277","author":"MG Crandall","year":"1983","unstructured":"Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton\u2013Jacobi equations. Trans. Am. Math. Soc. 277(1), 1\u201342 (1983). https:\/\/doi.org\/10.2307\/1999343","journal-title":"Trans. Am. Math. Soc."},{"issue":"13\u201316","key":"685_CR12","doi-asserted-by":"publisher","first-page":"1344","DOI":"10.1016\/j.cma.2005.05.023","volume":"195","author":"EJ Dean","year":"2006","unstructured":"Dean, E.J., Glowinski, R.: Numerical methods for fully nonlinear elliptic equations of the Monge\u2013Amp\u00e8re type. Comput. Methods Appl. Mech. Eng. 195(13\u201316), 1344\u20131386 (2006). https:\/\/doi.org\/10.1016\/j.cma.2005.05.023","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"283","key":"685_CR13","doi-asserted-by":"publisher","first-page":"1433","DOI":"10.1090\/S0025-5718-2012-02632-9","volume":"82","author":"K Debrabant","year":"2013","unstructured":"Debrabant, K., Jakobsen, E.R.: Semi-Lagrangian schemes for linear and fully non-linear diffusion equations. Math. Comput. 82(283), 1433\u20131462 (2013). https:\/\/doi.org\/10.1090\/S0025-5718-2012-02632-9","journal-title":"Math. Comput."},{"issue":"2","key":"685_CR14","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1137\/16M1061709","volume":"55","author":"X Feng","year":"2017","unstructured":"Feng, X., Jensen, M.: Convergent semi-Lagrangian methods for the Monge\u2013Amp\u00e8re equation on unstructured grids. SIAM J. Numer. Anal. 55(2), 691\u2013712 (2017)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"685_CR15","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1007\/s10915-008-9221-9","volume":"38","author":"X Feng","year":"2009","unstructured":"Feng, X., Neilan, M.: Vanishing moment method and moment solutions for fully nonlinear second order partial differential equations. J. Sci. Comput. 38(1), 74\u201398 (2009). https:\/\/doi.org\/10.1007\/s10915-008-9221-9","journal-title":"J. Sci. Comput."},{"issue":"2","key":"685_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.21314\/JCF.2007.163","volume":"11","author":"PA Forsyth","year":"2007","unstructured":"Forsyth, P.A., Labahn, G.: Numerical methods for controlled Hamilton\u2013Jacobi\u2013Bellman PDEs in finance. J. Comput. Finance 11(2), 1 (2007)","journal-title":"J. Comput. Finance"},{"issue":"4","key":"685_CR17","doi-asserted-by":"publisher","first-page":"1692","DOI":"10.1137\/100803092","volume":"49","author":"BD Froese","year":"2011","unstructured":"Froese, B.D., Oberman, A.M.: Convergent finite difference solvers for viscosity solutions of the elliptic Monge\u2013Amp\u00e8re equation in dimensions two and higher. SIAM J. Numer. Anal. 49(4), 1692\u20131714 (2011). https:\/\/doi.org\/10.1137\/100803092","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"685_CR18","doi-asserted-by":"publisher","first-page":"818","DOI":"10.1016\/j.jcp.2010.10.020","volume":"230","author":"BD Froese","year":"2011","unstructured":"Froese, B.D., Oberman, A.M.: Fast finite difference solvers for singular solutions of the elliptic Monge\u2013Amp\u00e8re equation. J. Comput. Phys. 230(3), 818\u2013834 (2011). https:\/\/doi.org\/10.1016\/j.jcp.2010.020","journal-title":"J. Comput. Phys."},{"issue":"1","key":"685_CR19","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1137\/120875065","volume":"51","author":"BD Froese","year":"2013","unstructured":"Froese, B.D., Oberman, A.M.: Convergent filtered schemes for the Monge\u2013Amp\u00e8re partial differential equation. SIAM J. Numer. Anal. 51(1), 423\u2013444 (2013). https:\/\/doi.org\/10.1137\/120875065","journal-title":"SIAM J. Numer. Anal."},{"key":"685_CR20","volume-title":"The Monge\u2013Amp\u00e8re Equation","author":"CE Guti\u00e9rrez","year":"2012","unstructured":"Guti\u00e9rrez, C.E.: The Monge\u2013Amp\u00e8re Equation, vol. 42. Springer, Berlin (2012)"},{"key":"685_CR21","volume-title":"Dynamic Programming and Markov Processes","author":"RA Howard","year":"1960","unstructured":"Howard, R.A.: Dynamic Programming and Markov Processes. The Technology Press of M.I.T, Cambridge (1960)"},{"key":"685_CR22","first-page":"111","volume":"17","author":"NV Krylov","year":"1972","unstructured":"Krylov, N.V.: The control of the solution of a stochastic integral equation. Teor. Verojatnost. i Primenen. 17, 111\u2013128 (1972)","journal-title":"Teor. Verojatnost. i Primenen."},{"issue":"4","key":"685_CR23","doi-asserted-by":"publisher","first-page":"A2025","DOI":"10.1137\/120887655","volume":"35","author":"O Lakkis","year":"2013","unstructured":"Lakkis, O., Pryer, T.: A finite element method for nonlinear elliptic problems. SIAM J. Sci. Comput. 35(4), A2025\u2013A2045 (2013). https:\/\/doi.org\/10.1137\/120887655","journal-title":"SIAM J. Sci. Comput."},{"key":"685_CR24","unstructured":"Lin, J.: Wide stencil for the Monge\u2013Amp\u00e8re equation. Technical report, University of Waterloo master essay, supervised by Justin WL Wan, https:\/\/uwaterloo.ca\/computational-mathematics\/sites\/ca.computational-mathematics\/files\/uploads\/files\/cmmain1.pdf (2014)"},{"key":"685_CR25","unstructured":"Lions, P.L.: Hamilton\u2013Jacobi\u2013Bellman equations and the optimal control of stochastic systems. In: Proceedings of the International Congress of Mathematicians, vol. 1, 2 (Warsaw, 1983), pp. 1403\u20131417. PWN, Warsaw (1984)"},{"key":"685_CR26","unstructured":"Ma, K., Forsyth, P.: An unconditionally monotone numerical scheme for the two factor uncertain volatility model. Preprint (2014)"},{"issue":"1","key":"685_CR27","doi-asserted-by":"publisher","first-page":"221","DOI":"10.3934\/dcdsb.2008.10.221","volume":"10","author":"AM Oberman","year":"2008","unstructured":"Oberman, A.M.: Wide stencil finite difference schemes for the elliptic Monge\u2013Amp\u00e8re equation and functions of the eigenvalues of the Hessian. Discrete Contin. Dyn. Syst. Ser. B 10(1), 221\u2013238 (2008). https:\/\/doi.org\/10.3934\/dcdsb.2008.10.221","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"issue":"3","key":"685_CR28","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/BF01396762","volume":"54","author":"VI Oliker","year":"1988","unstructured":"Oliker, V.I., Prussner, L.D.: On the numerical solution of the equation $$(\\partial ^2z\/\\partial x^2)(\\partial ^2z\/\\partial y^2)-((\\partial ^2z\/\\partial x\\partial y))^2=f$$ ( \u2202 2 z \/ \u2202 x 2 ) ( \u2202 2 z \/ \u2202 y 2 ) - ( ( \u2202 2 z \/ \u2202 x \u2202 y ) ) 2 = f and its discretizations. I. Numer. Math. 54(3), 271\u2013293 (1988). https:\/\/doi.org\/10.1007\/BF01396762","journal-title":"Numer. Math."},{"key":"685_CR29","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y Saad","year":"2003","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2003). https:\/\/doi.org\/10.1137\/1.9780898718003","edition":"2"},{"key":"685_CR30","doi-asserted-by":"publisher","DOI":"10.1201\/9780203908518","volume-title":"The Theory of Difference Schemes, Monographs and Textbooks in Pure and Applied Mathematics","author":"AA Samarskii","year":"2001","unstructured":"Samarskii, A.A.: The Theory of Difference Schemes, Monographs and Textbooks in Pure and Applied Mathematics, vol. 240. Marcel Dekker, Inc., New York (2001). https:\/\/doi.org\/10.1201\/9780203908518"},{"issue":"2","key":"685_CR31","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1137\/S0895479894276370","volume":"17","author":"PN Shivakumar","year":"1996","unstructured":"Shivakumar, P.N., Williams, J.J., Ye, Q., Marinov, C.A.: On two-sided bounds related to weakly diagonally dominant $$M$$ M -matrices with application to digital circuit dynamics. SIAM J. Matrix Anal. Appl. 17(2), 298\u2013312 (1996). https:\/\/doi.org\/10.1137\/S0895479894276370","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"685_CR32","unstructured":"Smears, I.: Hamilton\u2013Jacobi\u2013Bellman equations analysis and numerical analysis. Technical report, research report available on www.math.dur.ac.uk\/Ug\/projects\/highlights\/PR4\/Smears_HJB_report.pdf"},{"issue":"3","key":"685_CR33","doi-asserted-by":"publisher","first-page":"1580","DOI":"10.1137\/060675186","volume":"46","author":"J Wang","year":"2008","unstructured":"Wang, J., Forsyth, P.A.: Maximal use of central differencing for Hamilton\u2013Jacobi\u2013Bellman PDEs in finance. SIAM J. Numer. Anal. 46(3), 1580\u20131601 (2008). https:\/\/doi.org\/10.1137\/060675186","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-018-0685-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0685-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0685-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,28]],"date-time":"2020-10-28T23:21:14Z","timestamp":1603927274000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-018-0685-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,3]]},"references-count":33,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["685"],"URL":"https:\/\/doi.org\/10.1007\/s10915-018-0685-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2018,3,3]]},"assertion":[{"value":"11 May 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 November 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 March 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}