{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:22:22Z","timestamp":1776784942890,"version":"3.51.2"},"reference-count":21,"publisher":"American Mathematical Society (AMS)","issue":"254","license":[{"start":{"date-parts":[[2006,12,16]],"date-time":"2006-12-16T00:00:00Z","timestamp":1166227200000},"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":"

\n We study arbitrary-order Hermite difference methods for the numerical solution of initial-boundary value problems for symmetric hyperbolic systems. These differ from standard difference methods in that derivative data (or equivalently local polynomial expansions) are carried at each grid point. Time-stepping is achieved using staggered grids and Taylor series. We prove that methods using derivatives of order\n \n \n \n m<\/mml:mi>\n m<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n in each coordinate direction are stable under\n \n \n \n m<\/mml:mi>\n m<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n -independent CFL constraints and converge at order\n \n \n \n \n 2<\/mml:mn>\n m<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n 2m+1<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n . The stability proof relies on the fact that the Hermite interpolation process generally decreases a seminorm of the solution. We present numerical experiments demonstrating the resolution of the methods for large\n \n \n \n m<\/mml:mi>\n m<\/mml:annotation>\n <\/mml:semantics>\n <\/mml:math>\n <\/inline-formula>\n as well as illustrating the basic theoretical results.\n <\/p>","DOI":"10.1090\/s0025-5718-05-01808-9","type":"journal-article","created":{"date-parts":[[2006,2,15]],"date-time":"2006-02-15T11:05:20Z","timestamp":1140001520000},"page":"595-630","source":"Crossref","is-referenced-by-count":40,"title":["Hermite methods for hyperbolic initial-boundary value problems"],"prefix":"10.1090","volume":"75","author":[{"given":"John","family":"Goodrich","sequence":"first","affiliation":[]},{"given":"Thomas","family":"Hagstrom","sequence":"additional","affiliation":[]},{"given":"Jens","family":"Lorenz","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2005,12,16]]},"reference":[{"key":"1","isbn-type":"print","first-page":"3","article-title":"Dispersive properties of high order finite elements","author":"Ainsworth, Mark","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/354040127X"},{"key":"2","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1007\/BF02161845","article-title":"Piecewise Hermite interpolation in one and two variables with applications to partial differential equations","volume":"11","author":"Birkhoff, G.","year":"1968","journal-title":"Numer. 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