{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T08:40:18Z","timestamp":1762504818034},"reference-count":17,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2003,12,1]],"date-time":"2003-12-01T00:00:00Z","timestamp":1070236800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2003,12]]},"DOI":"10.1016\/s0096-3003(02)00472-1","type":"journal-article","created":{"date-parts":[[2003,1,30]],"date-time":"2003-01-30T14:29:44Z","timestamp":1043936984000},"page":"97-116","source":"Crossref","is-referenced-by-count":11,"title":["Collocation discretizations of the transport equation with radial basis functions"],"prefix":"10.1016","volume":"145","author":[{"given":"R.A.","family":"Lorentz","sequence":"first","affiliation":[]},{"given":"F.J.","family":"Narcowich","sequence":"additional","affiliation":[]},{"given":"J.D.","family":"Ward","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0096-3003(02)00472-1_BIB1","doi-asserted-by":"crossref","first-page":"787","DOI":"10.2307\/2154583","article-title":"Approximation from shift-invariant subspaces of L2(Rd)","volume":"341","author":"de Boor","year":"1994","journal-title":"Trans. Am. Math. Soc."},{"key":"10.1016\/S0096-3003(02)00472-1_BIB2","doi-asserted-by":"crossref","first-page":"1549","DOI":"10.1137\/S1064827500367609","article-title":"Fast Evaluation of radial basis functions: Methods for generalized multiquadrics in Rn","volume":"23","author":"Cherrie","year":"2002","journal-title":"SIAM J. Sci. Comp."},{"key":"10.1016\/S0096-3003(02)00472-1_BIB3","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s003659900104","article-title":"Variational principles and Sobolev-type estimates for generalized interpolation on a Riemannian manifold","volume":"15","author":"Dyn","year":"1999","journal-title":"Constr. Approx."},{"key":"10.1016\/S0096-3003(02)00472-1_BIB4","series-title":"Surface Fitting and Multiresolution Methods","first-page":"131","article-title":"Solving partial differential equations by collocation with radial basis functions","author":"Fasshauer","year":"1997"},{"key":"10.1016\/S0096-3003(02)00472-1_BIB5","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0096-3003(97)10104-7","article-title":"Solving partial differential equations by collocation using radial basis functions","volume":"93","author":"Franke","year":"1998","journal-title":"Appl. Math. Computat."},{"key":"10.1016\/S0096-3003(02)00472-1_BIB6","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/0021-9045(68)90055-5","article-title":"Approximation by periodic spline interpolants on uniform meshes","volume":"1","author":"Golomb","year":"1968","journal-title":"J. Approx. Theory"},{"key":"10.1016\/S0096-3003(02)00472-1_BIB7","doi-asserted-by":"crossref","unstructured":"D. Gottlieb, S.A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, CBMS\u2013NSF Regional Conference Series in Applied Mathematics, no. 26, SIAM, Philadelphia, 1977","DOI":"10.1137\/1.9781611970425"},{"key":"10.1016\/S0096-3003(02)00472-1_BIB8","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0898-1221(90)90272-L","article-title":"Theory and applications of the multiquadric-biharmonic method","volume":"19","author":"Hardy","year":"1990","journal-title":"Comp. Math. Appl."},{"issue":"1","key":"10.1016\/S0096-3003(02)00472-1_BIB9","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1023\/A:1025606420187","article-title":"A Multiquadric interpolation method for solving initial value problems","volume":"12","author":"Hon","year":"1997","journal-title":"Sci. Comp."},{"key":"10.1016\/S0096-3003(02)00472-1_BIB10","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0898-1221(90)90271-K","article-title":"Multiquadrics\u2013\u2013a scattered data approximation scheme with applications to computational fluid dynamics\u2013\u2013II. Solutions to parabolic, hyperbolic and elliptic partial differential equations","volume":"19","author":"Kansa","year":"1990","journal-title":"Comp. Math. Appl."},{"key":"10.1016\/S0096-3003(02)00472-1_BIB11","series-title":"An Introduction to Harmonic Analysis","author":"Katznelson","year":"1976"},{"key":"10.1016\/S0096-3003(02)00472-1_BIB12","first-page":"221","article-title":"Recent developments in approximation via positive definite functions","volume":"vol. 2","author":"Narcowich","year":"1998"},{"key":"10.1016\/S0096-3003(02)00472-1_BIB13","series-title":"Numerical Approximation of Partial Differential Equations","author":"Quarteroni","year":"1991"},{"key":"10.1016\/S0096-3003(02)00472-1_BIB14","series-title":"Difference Methods for Initial Value Problems","author":"Richtmeyer","year":"1967"},{"key":"10.1016\/S0096-3003(02)00472-1_BIB15","doi-asserted-by":"crossref","unstructured":"A. Ron, The L2-approximation orders of principal shift-invariant spaces generated by radial basis function, in: D. Braess, L. Schumaker (Eds.), Numerical Methods of approximation Theory, Birkh\u00e4user, Basel, pp. 1\u201324","DOI":"10.1007\/978-3-0348-8619-2_14"},{"key":"10.1016\/S0096-3003(02)00472-1_BIB16","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/BF02123482","article-title":"Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree","volume":"4","author":"Wendland","year":"1995","journal-title":"Adv. Comp. Math."},{"key":"10.1016\/S0096-3003(02)00472-1_BIB17","doi-asserted-by":"crossref","first-page":"1521","DOI":"10.1090\/S0025-5718-99-01102-3","article-title":"Meshless Galerkin methods using radial basis functions","volume":"68","author":"Wendland","year":"1999","journal-title":"Math. Comp."}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300302004721?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300302004721?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,30]],"date-time":"2019-03-30T07:54:47Z","timestamp":1553932487000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300302004721"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,12]]}},"alternative-id":["S0096300302004721"],"URL":"https:\/\/doi.org\/10.1016\/s0096-3003(02)00472-1","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2003,12]]}}}