{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T00:41:23Z","timestamp":1774658483357,"version":"3.50.1"},"reference-count":17,"publisher":"American Mathematical Society (AMS)","issue":"227","license":[{"start":{"date-parts":[[2000,2,5]],"date-time":"2000-02-05T00:00:00Z","timestamp":949708800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Hermite approximation is investigated. Some inverse inequalities, imbedding inequalities and approximation results are obtained. A Hermite spectral scheme is constructed for Burgers equation. The stability and convergence of the proposed scheme are proved strictly. The techniques used in this paper are also applicable to other nonlinear problems in unbounded domains.<\/p>","DOI":"10.1090\/s0025-5718-99-01059-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:14:44Z","timestamp":1027721684000},"page":"1067-1078","source":"Crossref","is-referenced-by-count":110,"title":["Error estimation of Hermite spectral method for nonlinear partial differential equations"],"prefix":"10.1090","volume":"68","author":[{"given":"Ben-yu","family":"Guo","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1999,2,5]]},"reference":[{"key":"1","unstructured":"Y. Maday, B. Pernaud-Thomas and H. Vandeven, One r\u00e9habilitation des m\u00e9thodes spectrales de type Laguerre, Rech. A\u00e9rospat., 6 (1985), 353-379."},{"key":"2","doi-asserted-by":"crossref","unstructured":"O. Coulaud, D. Funaro and O. Kavian, Laguerre spectral approximation of elliptic problems in exterior domains, Comput. Methods Appl. Mech. Engrg., 80 (1990), 451-458.","DOI":"10.1016\/0045-7825(90)90050-V"},{"key":"3","first-page":"263","article-title":"Estimates of Laguerre spectral projectors in Sobolev spaces","author":"Funaro, Daniele","year":"1991"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/0045-7825(92)90171-F","article-title":"Some spectral approximations for differential equations in unbounded domains","volume":"98","author":"Iranzo, V.","year":"1992","journal-title":"Comput. Methods Appl. Mech. Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/0045-7825","issn-type":"print"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1016\/0021-9991(89)90112-5","article-title":"Laguerre polynomials for infinite-domain spectral elements","volume":"80","author":"Mavriplis, Cathy","year":"1989","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"key":"6","unstructured":"K. Black, Spectral elements on infinite domains (unpublished)."},{"issue":"196","key":"7","doi-asserted-by":"publisher","first-page":"597","DOI":"10.2307\/2938707","article-title":"Approximation of some diffusion evolution equations in unbounded domains by Hermite functions","volume":"57","author":"Funaro, Daniele","year":"1991","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/BF01385518","article-title":"The eigenvalues of Hermite and rational spectral differentiation matrices","volume":"61","author":"Weideman, J. A. C.","year":"1992","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"6","key":"9","doi-asserted-by":"publisher","first-page":"1337","DOI":"10.1137\/0142093","article-title":"A complete orthonormal system of functions in \ud835\udc3f\u00b2(-\u221e,\u221e) space","volume":"42","author":"Christov, C. I.","year":"1982","journal-title":"SIAM J. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1399","issn-type":"print"},{"issue":"1","key":"10","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/0021-9991(87)90158-6","article-title":"Spectral methods using rational basis functions on an infinite interval","volume":"69","author":"Boyd, John P.","year":"1987","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"key":"11","series-title":"Pure and Applied Mathematics, Vol. 65","volume-title":"Sobolev spaces","author":"Adams, Robert A.","year":"1975"},{"key":"12","unstructured":"R. J. Nessel and G. Wilmes, On Nikolskii-type inequalities for orthogonal expansion, in Approximation Theory II , ed. by G. G. Lorentz, C. K. Chui and L. L. Schumaker, Academic Press, New York, 479-484."},{"key":"13","doi-asserted-by":"crossref","unstructured":"R. Courant, K. O. Friedrichs and H. Lewy, \u00dcber die partiellen differezengleichungen der mathematischen physik, Math. Ann.,  100 (1928), 32-74.","DOI":"10.1007\/BF01448839"},{"issue":"4","key":"14","first-page":"242","article-title":"A certain class of finite difference schemes for the two-dimensional vorticity equation of a viscous fluid","volume":"17","author":"Kuo, P\u00ean Y\u00fc","year":"1974","journal-title":"Acta Math. Sinica","ISSN":"https:\/\/id.crossref.org\/issn\/0583-1431","issn-type":"print"},{"key":"15","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1090\/conm\/163\/01548","article-title":"Generalized stability of discretization and its applications to numerical solutions of nonlinear differential equations","author":"Guo, Ben Yu","year":"1994"},{"key":"16","first-page":"111","article-title":"Stability of nonlinear discretization algorithms","author":"Stetter, Hans J.","year":"1966"},{"key":"17","first-page":"623","article-title":"Annihilator ideals and representation iteration for abstract rings","volume":"5","author":"Everett, C. J., Jr.","year":"1939","journal-title":"Duke Math. J.","ISSN":"https:\/\/id.crossref.org\/issn\/0012-7094","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1999-68-227\/S0025-5718-99-01059-5\/S0025-5718-99-01059-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1999-68-227\/S0025-5718-99-01059-5\/S0025-5718-99-01059-5.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T00:05:57Z","timestamp":1635897957000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1999-68-227\/S0025-5718-99-01059-5\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,2,5]]},"references-count":17,"journal-issue":{"issue":"227","published-print":{"date-parts":[[1999,7]]}},"alternative-id":["S0025-5718-99-01059-5"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-99-01059-5","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0025-5718","1088-6842"],"issn-type":[{"value":"0025-5718","type":"print"},{"value":"1088-6842","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,2,5]]}}}