{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:16:08Z","timestamp":1776842168202,"version":"3.51.2"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2005,5,1]],"date-time":"2005-05-01T00:00:00Z","timestamp":1114905600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2005,5]]},"DOI":"10.1007\/s10444-003-3960-9","type":"journal-article","created":{"date-parts":[[2005,2,16]],"date-time":"2005-02-16T17:44:03Z","timestamp":1108575843000},"page":"377-397","source":"Crossref","is-referenced-by-count":31,"title":["Approximation of parabolic PDEs on spheres using spherical basis functions"],"prefix":"10.1007","volume":"22","author":[{"given":"Q. T.","family":"Le Gia","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"CR1","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1137\/S1064827595281344","volume":"18","author":"J. Cui","year":"1997","unstructured":"J. Cui and W. Freeden, Equidistribution on the sphere, SIAM J. Sci. Statist. Comput. 18 (1997) 595?609.","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"CR2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198536826.001.0001","volume-title":"Constructive Approximation on the Sphere with Applications to Geomathematics","author":"W. Freeden","year":"1998","unstructured":"W. Freeden, T. Gervens and M. Schreiner, Constructive Approximation on the Sphere with Applications to Geomathematics (Oxford Univ. Press, Oxford, 1998)."},{"key":"CR3","unstructured":"J. G\u00f6ttelmann, A spline collocation scheme for the spherical shallow water equations, Preprint."},{"key":"CR4","unstructured":"S. Hubbert and T.M. Morton, Lp error estimates for radial basis function interpolation on the sphere, Preprint."},{"key":"CR5","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1090\/S0025-5718-99-01080-7","volume":"68","author":"K. Jetter","year":"1999","unstructured":"K. Jetter, J. Stockler and J.D. Ward, Error estimates for scattered data interpolation on spheres, Math. Comp. 68 (1999) 733?747.","journal-title":"Math. Comp."},{"key":"CR6","doi-asserted-by":"crossref","first-page":"2127","DOI":"10.1090\/S0002-9939-99-04683-3","volume":"127","author":"J. Levesley","year":"1999","unstructured":"J. Levesley, Z. Lou and X. Sun, Norm estimates of interpolation matrices and their inverses associated with strictly positive definite functions, Proc. Amer. Math. Soc. 127 (1999) 2127?2137.","journal-title":"Proc. Amer. Math. Soc."},{"key":"CR7","volume-title":"Nonhomogeneous Boundary Value Problems and Applications, Vol. I","author":"J.L. Lions","year":"1972","unstructured":"J.L. Lions and E. Magenes, Nonhomogeneous Boundary Value Problems and Applications, Vol. I (Springer, New York, 1972)."},{"key":"CR8","series-title":"Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-11761-3","volume-title":"Formulas and Theorems for the Special Functions of Mathematical Physics","author":"W. Magnus","year":"1966","unstructured":"W. Magnus, F. Oberhettinger and R.P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Bd. 52 (Springer, Berlin, 1966)."},{"issue":"2","key":"CR9","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1006\/jath.2001.3642","volume":"114","author":"T.M. Morton","year":"2002","unstructured":"T.M. Morton and M. Neamtu, Error bounds for solving pseudodifferential equations on spheres by collocation with zonal kernels, J. Approx. Theory 114(2) (2002) 242?268.","journal-title":"J. Approx. Theory"},{"key":"CR10","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0094775","volume-title":"Spherical Harmonics","author":"C. M\u00fcller","year":"1966","unstructured":"C. M\u00fcller, Spherical Harmonics, Lecture Notes in Mathematics, Vol. 17 (Springer, Berlin, 1966)."},{"key":"CR11","volume-title":"Fundamentals of Differential Equations","author":"R. Nagle","year":"2000","unstructured":"R. Nagle, E. Saff and A. Snider, Fundamentals of Differential Equations (Addison-Wesley, New York, 2000)."},{"key":"CR12","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1023\/A:1018996230401","volume":"8","author":"F.J. Narcowich","year":"1998","unstructured":"F.J. Narcowich, N. Sivakumar and J.D. Ward, Stability results for scattered-data interpolation on Euclidean spheres, Adv. Comput. Math. 8 (1998) 137?163.","journal-title":"Adv. Comput. Math."},{"issue":"6","key":"CR13","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1137\/S0036141001395054","volume":"33","author":"F.J. Narcowich","year":"2002","unstructured":"F.J. Narcowich and J.D. Ward, Scattered-data interpolation on spheres: Error estimates and locally supported basis functions, SIAM J. Math. Anal. 33(6) (2002) 1393?1410.","journal-title":"SIAM J. Math. Anal."},{"key":"CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0953-9","volume-title":"Partial Differential Equations","author":"J. Rauch","year":"1991","unstructured":"J. Rauch, Partial Differential Equations (Springer, New York, 1991)."},{"key":"CR15","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF03024331","volume":"19","author":"E.B. Saff","year":"1997","unstructured":"E.B. Saff and A.B.J. Kuijlaars, Distributing many points on a sphere, Math. Intelligencer 19 (1997) 5?11.","journal-title":"Math. Intelligencer"},{"key":"CR16","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1215\/S0012-7094-42-00908-6","volume":"9","author":"I.J. Schoenberg","year":"1942","unstructured":"I.J. Schoenberg, Positive definite functions on spheres, Duke Math. J. 9 (1942) 96?108.","journal-title":"Duke Math. J."},{"key":"CR17","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/0021-9045(84)90066-2","volume":"40","author":"S.L. Svensson","year":"1984","unstructured":"S.L. Svensson, Finite elements on the sphere, J. Approx. Theory 40 (1984) 246?260.","journal-title":"J. Approx. Theory"},{"key":"CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF03654992","volume":"8","author":"S.L. Svensson","year":"1983","unstructured":"S.L. Svensson, Pseudodifferential operators ? a new approach to the boundary value problems of physical geodesy, Manuscr. Geod. 8 (1983) 1?40.","journal-title":"Manuscr. Geod."},{"key":"CR19","series-title":"Lecture Notes in Mathematics","volume-title":"Galerkin Finite Element Methods for Parabolic Problems","author":"V. Thom\u00e9e","year":"1984","unstructured":"V. Thom\u00e9e, Galerkin Finite Element Methods for Parabolic Problems, Lecture Notes in Mathematics, Vol. 1054 (Springer, Berlin, 1984)."},{"key":"CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0377-0427(00)00507-0","volume":"128","author":"V. Thom\u00e9e","year":"2001","unstructured":"V. Thom\u00e9e, From finite differences to finite elements, short history of numerical analysis of partial differential equations, J. Comput. Appl. Math. 128 (2001) 1?54.","journal-title":"J. Comput. Appl. Math."},{"key":"CR21","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/BF02123482","volume":"4","author":"H. Wendland","year":"1995","unstructured":"H. Wendland, Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree, Adv. Comput. Math. 4 (1995) 389?396.","journal-title":"Adv. Comput. Math."},{"key":"CR22","volume-title":"The Algebraic Eigenvalue Problem","author":"J.H. Wilkinson","year":"1965","unstructured":"J.H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1965)."},{"key":"CR23","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/S0021-9991(05)80016-6","volume":"102","author":"D.L. Williamson","year":"1992","unstructured":"D.L. Williamson et al., A standard test for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211?224.","journal-title":"J. Comput. Phys."},{"key":"CR24","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1090\/S0002-9939-1992-1096214-6","volume":"116","author":"Y. Xu","year":"1992","unstructured":"Y. Xu and E.W. Cheney, Strictly positive definite functions on spheres, Proc. Amer. Math. Soc. 116 (1992) 977?981.","journal-title":"Proc. Amer. Math. Soc."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-003-3960-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-003-3960-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-003-3960-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,23]],"date-time":"2024-12-23T10:30:46Z","timestamp":1734949846000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-003-3960-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,5]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,5]]}},"alternative-id":["5253960"],"URL":"https:\/\/doi.org\/10.1007\/s10444-003-3960-9","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,5]]}}}