{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T03:16:45Z","timestamp":1787541405428,"version":"build-2736575974"},"reference-count":4,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1996,5]]},"abstract":"<jats:p>The temporal integration of hyperbolic partial differential equations (PDEs) has been shown to lead sometimes to the deterioration of accuracy of the solution because of boundary conditions. A procedure for removal of this error in the linear case has been established previously.<\/jats:p>\n                  <jats:p>In this paper we consider hyperbolic PDEs (linear and nonlinear) whose boundary treatment is accomplished via the simultaneous approximation term (SAT) procedure. A methodology is presented for recovery of the full order of accuracy and has been applied to the case of a fourth-order explicit finite-difference scheme.<\/jats:p>","DOI":"10.1137\/s1064827595282520","type":"journal-article","created":{"date-parts":[[2005,3,1]],"date-time":"2005-03-01T03:43:46Z","timestamp":1109648626000},"page":"777-782","source":"Crossref","is-referenced-by-count":42,"title":["On the Removal of Boundary Errors Caused by Runge\u2013Kutta Integration of Nonlinear Partial Differential Equations"],"prefix":"10.1137","volume":"17","author":[{"given":"Saul","family":"Abarbanel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Gottlieb","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mark H.","family":"Carpenter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.3402\/tellusa.v24i3.10634"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0916072"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1057"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(93)90112-5"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827595282520","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:42:08Z","timestamp":1787334128000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827595282520"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,5]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1996,5]]}},"alternative-id":["10.1137\/S1064827595282520"],"URL":"https:\/\/doi.org\/10.1137\/s1064827595282520","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,5]]}}}