{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T10:24:15Z","timestamp":1789727055005,"version":"4.0.1"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9550-16-1-0102"],"award-info":[{"award-number":["FA9550-16-1-0102"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["MURI W911NF-15-1-0562"],"award-info":[{"award-number":["MURI W911NF-15-1-0562"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371298"],"award-info":[{"award-number":["11371298"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91630204"],"award-info":[{"award-number":["91630204"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1620262"],"award-info":[{"award-number":["DMS-1620262"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Numerical approximations of fractional PDEs in unbounded domains are considered in this paper. Since their solutions decay slowly with power laws at infinity, a domain truncation approach is not effective as no transparent boundary condition is available. We develop efficient Hermite-collocation and Hermite--Galerkin methods for solving a class of fractional PDEs in unbounded domains directly, and derive corresponding error estimates. We apply these methods for solving fractional advection-diffusion equations and fractional nonlinear Schr\u00f6dinger equations.<\/jats:p>","DOI":"10.1137\/16m1097109","type":"journal-article","created":{"date-parts":[[2017,9,12]],"date-time":"2017-09-12T10:49:46Z","timestamp":1505213386000},"page":"A1928-A1950","source":"Crossref","is-referenced-by-count":73,"title":["Hermite Spectral Methods for Fractional PDEs in Unbounded Domains"],"prefix":"10.1137","volume":"39","author":[{"given":"Zhiping","family":"Mao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Shen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,9,12]]},"reference":[{"key":"atypb1","unstructured":"R.A. Adams,\n                      Sobolev Spaces\n                      , Acadmic Press, New York, 1975."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.09.013"},{"key":"atypb3","first-page":"211","volume-title":"L\u00e9vy motion, and the made tracer tests, in Dispersion in Heterogeneous Geological Formations","author":"Benson D.A.","year":"2002"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1029\/2000WR900031"},{"key":"atypb5","volume-title":"Chebyshev and Fourier Spectral Methods","author":"Boyd J.P.","year":"2001"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1090\/mcom3035"},{"key":"atypb7","volume-title":"Grad. Stud. Math. 29","author":"Duoandikoetxea J.","year":"2001"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198506720.001.0001"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(79)90097-4"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.07.026"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2014.0364"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386067"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2016.04.002"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-008-9184-9"},{"key":"atypb15","volume-title":"Gordon and Breach","author":"Samko S.G.","year":"1993"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1029\/2008JF001246"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71041-7"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/0915089"},{"key":"atypb19","doi-asserted-by":"crossref","first-page":"195","DOI":"10.4208\/cicp.2009.v5.p195","volume":"5","author":"Shen J.","year":"2009","journal-title":"Commun. Comput. Phys."},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-068650-6.50030-7"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1137\/0914038"},{"key":"atypb22","first-page":"167","volume":"22","author":"Xu C.-L.","year":"2003","journal-title":"Comput. Appl. Math."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2013.06.031"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1137\/130933216"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1097109","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:05:38Z","timestamp":1787328338000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1097109"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":24,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1097109"],"URL":"https:\/\/doi.org\/10.1137\/16m1097109","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}