{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T11:13:42Z","timestamp":1791198822824,"version":"4.1.0"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>The stability of five finite difference\u2013time domain (FD\u2013TD) schemes coupling Maxwell equations to Debye or Lorentz models has been analyzed in [P. Petropoulos, Stability and phase error analysis of FD\u2013TD in dispersive dielectrics, IEEE Trans. Antennas Propag., 42 (1994), pp. 62\u201369], where numerical evidence for specific media have been used. We use von Neumann analysis to give necessary and sufficient stability conditions for these schemes for any medium, in accordance with the partial results of [P. Petropoulos, Stability and phase error analysis of FD\u2013TD in dispersive dielectrics, IEEE Trans. Antennas Propag., 42 (1994), pp. 62\u201369]. To make this approach tractable for two-dimensional and three-dimensional models, we have developed a computer algebra environment which has a wider range of applicability.<\/jats:p>","DOI":"10.1137\/060671255","type":"journal-article","created":{"date-parts":[[2008,6,18]],"date-time":"2008-06-18T18:02:38Z","timestamp":1213812158000},"page":"2551-2566","source":"Crossref","is-referenced-by-count":16,"title":["Stability of FD\u2013TD Schemes for Maxwell\u2013Debye and Maxwell\u2013Lorentz Equations"],"prefix":"10.1137","volume":"46","author":[{"given":"Brigitte","family":"Bid\u00e9garay-Fesquet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,6,18]]},"reference":[{"key":"R1","unstructured":"B. Bid\u00e9garay-Fesquet,\n                      Von Neumann Stability Analysis of Finite Difference Schemes for Maxwell\u2013Debye and Maxwell\u2013Lorentz Equations\n                      , English translation of Technical report 1077-M, LMC-IMAG, available online at http:\/\/hal.ccsd.cnrs.fr\/ccsd-00005369 (2005)."},{"key":"R2","unstructured":"B. Bid\u00e9garay-Fesquet,\n                      NAUtil: von Neumann Analysis Utilities\n                      , Maple Toolbox, available online at http:\/\/ljk.imag.fr\/membres\/Brigitte.Bidegaray\/NAUtil\/ (2006)."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.2004.835274"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1364\/OL.16.001412"},{"key":"R5","first-page":"1326","volume":"73","author":"Kashiwa T.","year":"1990","journal-title":"IEICE Trans."},{"key":"R6","doi-asserted-by":"crossref","unstructured":"R. Liska and L. Drsda,\n                      FIDE; a REDUCE package for automation of FInite difference method for solving pDE\n                      , in Proceedings of the International Symposium on Symbolic and Algebraic Computation, Tokyo, Japan, 1990, ACM Press, 1990, pp. 169\u2013176.","DOI":"10.1145\/96877.96920"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1109\/15.57116"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1109\/8.247751"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/8.3.397"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1109\/8.272302"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(96)00039-0"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2003.816083"},{"key":"R13","unstructured":"J. Strikwerda,\n                      Finite Difference Schemes and Partial Differential Equations\n                      , Wadsworth & Brooks\/Cole, Wadsworth, CA, 1989."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.1966.1138693"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1109\/8.376042"},{"key":"R16","unstructured":"J. L. Young,\n                      Finite difference time\u2013domain methodologies for electromagnetic wave propagation in complex media\n                      , in Frontiers in Electromagnetics, D. H. Werner and R. Mittra, eds., IEEE Press, Piscataway, NJ, 2000, pp. 666\u2013707."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1109\/8.376042"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060671255","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:27Z","timestamp":1787325267000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060671255"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":17,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060671255"],"URL":"https:\/\/doi.org\/10.1137\/060671255","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}