{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:34:23Z","timestamp":1787330063510,"version":"3.56.0"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>We present a monotone waveform relaxation algorithm which produces very tight upper and lower bounds of the transient response of a class of systems described by nonlinear differential-algebraic equations (DAEs) that satisfy certain Lipschitz conditions. The choice of initial iteration is critical and we give two methods of finding it. We show that the class of systems in which monotone convergence of waveform relaxation is possible is actually larger than previously reported. Numerical experiments are given to confirm the monotonicity of convergence of the algorithm.<\/jats:p>","DOI":"10.1137\/s0036142998348765","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"170-185","source":"Crossref","is-referenced-by-count":18,"title":["Monotone Waveform Relaxation for Systems of Nonlinear Differential-Algebraic Equations"],"prefix":"10.1137","volume":"38","author":[{"given":"Yao-Lin","family":"Jiang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Omar","family":"Wing","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.1983.1270037"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.1986.1270200"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0908046"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.1982.1270004"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/0917011"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142995294292"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(93)90049-W"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759528778X"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142992233098"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S003614299528002X"},{"key":"R11","unstructured":"Y. L. Jiang and O. Wing,\n                      Splitting techniques to speed up the convergence of waveform relaxation methods for tightly coupled circuit systems\n                      , in Proceedings of the 1997 European Conference on Circuit Theory and Design, Budapest, 1997, pp. 1054\u20131058."},{"key":"R12","first-page":"1961","volume":"80","author":"Jiang Y. L.","year":"1997","journal-title":"IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences"},{"key":"R13","first-page":"685","volume":"81","author":"Jiang Y. L.","year":"1998","journal-title":"IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1985.1085597"},{"key":"R15","unstructured":"I. W. Sandberg,\n                      A nonnegativity\u2010preservation property associated with certain systems of nonlinear differential equations\n                      , in Proceedings of the 1974 IEEE International Conference on Systems, Man and Cybernetics, IEEE Computer Society, Los Alamitas, CA, 1974, pp. 230\u2013233."},{"key":"R16","doi-asserted-by":"crossref","unstructured":"Y. L. Jiang and O. Wing,\n                      A necessary and sufficient condition for the convergence of iterative procedures for solving equations of nonlinear monotone resistive networks\n                      , in Proceedings of the 1997 IEEE International Symposium on Circuits and Systems, Vol. 2, Hong Kong, 1997, pp. 861\u2013864.","DOI":"10.1109\/ISCAS.1997.621849"},{"key":"R17","unstructured":"V. V. Nemytskii and V. V. Stepanov,\n                      Qualitative Theory of Differential Equations\n                      , Princeton University Press, Princeton, NJ, 1960."},{"key":"R18","doi-asserted-by":"crossref","unstructured":"D. Bainov and P. Simeonov,\n                      Integral Inequalities and Applications\n                      , Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992.","DOI":"10.1007\/978-94-015-8034-2"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5308"},{"key":"R20","unstructured":"Y. L. Jiang and O. Wing,\n                      Convergence conditions of waveform relaxation methods for circuit simulation\n                      , in Proceedings of the 1998 IEEE International Symposium on Circuits and Systems, Vol. VI, Monterey, CA, 1998, pp. 232\u2013235."},{"key":"R21","volume-title":"Monotone iterative techniques for nonlinear differential equations","author":"Ladde G.","year":"1985"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0036142998348765","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:45:39Z","timestamp":1787327139000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0036142998348765"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S0036142998348765"],"URL":"https:\/\/doi.org\/10.1137\/s0036142998348765","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}