{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T15:35:23Z","timestamp":1726068923910},"reference-count":25,"publisher":"Elsevier BV","issue":"8","license":[{"start":{"date-parts":[[2006,4,1]],"date-time":"2006-04-01T00:00:00Z","timestamp":1143849600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":2664,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers & Mathematics with Applications"],"published-print":{"date-parts":[[2006,4]]},"DOI":"10.1016\/j.camwa.2006.04.009","type":"journal-article","created":{"date-parts":[[2006,7,18]],"date-time":"2006-07-18T11:13:15Z","timestamp":1153221195000},"page":"1335-1348","source":"Crossref","is-referenced-by-count":70,"title":["The role of the multiquadric shape parameters in solving elliptic partial differential equations"],"prefix":"10.1016","volume":"51","author":[{"given":"J.","family":"Wertz","sequence":"first","affiliation":[]},{"given":"E.J.","family":"Kansa","sequence":"additional","affiliation":[]},{"given":"L.","family":"Ling","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"3\u20135","key":"10.1016\/j.camwa.2006.04.009_bib1","first-page":"491","article-title":"Improved multiquadric method for elliptic partial differential equations via PDE collocation on the boundary","volume":"43","author":"Fedoseyev","year":"2002","journal-title":"Computers Math. Applic."},{"key":"10.1016\/j.camwa.2006.04.009_bib2","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1002\/num.10062","article-title":"Exponential convergence and h-c multiquadric collocation method for partial differential equations","volume":"19","author":"Cheng","year":"2003","journal-title":"Num. Meth. PDEs"},{"key":"10.1016\/j.camwa.2006.04.009_bib3","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s00466-002-0357-4","article-title":"Development of RBF-DQ method for derivative approximation and its application to simulate natural convection in concentric annuli","volume":"29","author":"Wu","year":"2002","journal-title":"Comput. Mech."},{"key":"10.1016\/j.camwa.2006.04.009_bib4","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1016\/S0045-7825(02)00618-7","article-title":"Local radial basis function based differential quadrature method and its applications to solve two-dimensional incompressible Navier-Stokes equations","volume":"192","author":"Shu","year":"2003","journal-title":"Comput. Meth. Appl. Mech. Engng."},{"key":"10.1016\/j.camwa.2006.04.009_bib5","first-page":"77","article-title":"Multivariate interpolation and conditionally positive definite functions, Ap-prox","volume":"4","author":"Madych","year":"1988","journal-title":"Theory Appl."},{"issue":"12","key":"10.1016\/j.camwa.2006.04.009_bib6","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/0898-1221(92)90175-H","article-title":"Miscellaneous error bounds for multiquadric and related interpolators","volume":"24","author":"Madych","year":"1992","journal-title":"Computers Math. Applic."},{"issue":"6\u20138","key":"10.1016\/j.camwa.2006.04.009_bib7","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0898-1221(90)90271-K","article-title":"Multiquadrics-A scattered data approximation scheme with applications to computational fluid dynamics: H. Solutions to parabolic, hyperbolic, and elliptic partial differential equations","volume":"19","author":"Kansa","year":"1990","journal-title":"Computers Math. Applic."},{"key":"10.1016\/j.camwa.2006.04.009_bib8","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/S0955-7997(96)00033-1","article-title":"Improved multiquadric approximation for partial differential equations","volume":"18","author":"Golberg","year":"1996","journal-title":"Eng. Anal. Bound. Elem."},{"key":"10.1016\/j.camwa.2006.04.009_bib9","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1029\/JB076i008p01905","article-title":"Multiquadric equations of topography and other irregular surfaces","volume":"76","author":"Hardy","year":"1971","journal-title":"J. Geophys. Res."},{"issue":"8","key":"10.1016\/j.camwa.2006.04.009_bib10","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1016\/0898-1221(87)90043-5","article-title":"Interpolation and approximation of 3-D and 4-D scattered data","volume":"13","author":"Foley","year":"1987","journal-title":"Computers Math. Applic."},{"issue":"9","key":"10.1016\/j.camwa.2006.04.009_bib11","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0898-1221(91)90123-L","article-title":"The parameter R2 in multiquadric interpolation","volume":"21","author":"Carlson","year":"1991","journal-title":"Computers Math. Applic."},{"issue":"12","key":"10.1016\/j.camwa.2006.04.009_bib12","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0898-1221(92)90174-G","article-title":"Improved accuracy of multiquadric interpolation using variable shape parameters","volume":"24","author":"Kansa","year":"1992","journal-title":"Computers Math. Applic."},{"key":"10.1016\/j.camwa.2006.04.009_bib13","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1023\/A:1018975909870","article-title":"An algorithm for selecting a good value for the parameter c in radial basis functions interpolation","volume":"11","author":"Rippa","year":"1999","journal-title":"Adv. Comp. Math."},{"issue":"7\/8","key":"10.1016\/j.camwa.2006.04.009_bib14","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0898-1221(00)00071-7","article-title":"Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations","volume":"39","author":"Kansa","year":"2000","journal-title":"Computers Math. Applic."},{"issue":"3\u20135","key":"10.1016\/j.camwa.2006.04.009_bib15","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/S0898-1221(01)00295-4","article-title":"Interpolation in the limit of increasingly.at radial basis functions","volume":"43","author":"Driscoll","year":"2002","journal-title":"Computers Math. Applic."},{"issue":"5\/6","key":"10.1016\/j.camwa.2006.04.009_bib16","first-page":"891","article-title":"A numerical study of some radial basis function based solution methods for elliptic PDEs","volume":"46","author":"Fornberg","year":"2003","journal-title":"Computers Math. Applic."},{"issue":"1","key":"10.1016\/j.camwa.2006.04.009_bib17","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/S0898-1221(04)90004-1","article-title":"Some observations regarding interpolants in the limit of at radial basis functions","volume":"47","author":"Fornberg","year":"2004","journal-title":"Computers Math. Applic."},{"issue":"1","key":"10.1016\/j.camwa.2006.04.009_bib18","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.camwa.2005.01.010","article-title":"Theoretical and computational aspects of multivariate interpolation with increasingly at radial basis functions","volume":"49","author":"Larsson","year":"2005","journal-title":"Computers Math. Applic."},{"key":"10.1016\/j.camwa.2006.04.009_bib19","doi-asserted-by":"crossref","first-page":"2611","DOI":"10.1016\/S0045-7825(01)00419-4","article-title":"On the optimal shape parameters of radial basis functions used for 2-D meshless methods","volume":"191","author":"Wang","year":"2002","journal-title":"Comput. Meth. Appl. Mech. Eng."},{"key":"10.1016\/j.camwa.2006.04.009_bib20","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/s00466-003-0433-4","article-title":"A local Heaviside weighted meshless method for two-dimensional solids using radial basis functions","volume":"31","author":"Xiao","year":"2003","journal-title":"Computat. Mech."},{"key":"10.1016\/j.camwa.2006.04.009_bib21","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.enganabound.2004.12.004","article-title":"Meshless solutions of 2D contact problems by subdomain variational inequality and MLPG method with radial basis functions","volume":"29","author":"Xiao","year":"2005","journal-title":"Eng. Anal. Bound. Elem."},{"key":"10.1016\/j.camwa.2006.04.009_bib22","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10444-004-1809-5","article-title":"A least squares preconditioner for radial basis functions collocation methods","volume":"23","author":"Ling","year":"2005","journal-title":"Adv. Comput. Math."},{"issue":"13","key":"10.1016\/j.camwa.2006.04.009_bib23","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1016\/j.mcm.2005.01.002","article-title":"Preconditioning for radial basis functions with domain decomposition","volume":"40","author":"Ling","year":"2004","journal-title":"Mathl. Comput. Modelling"},{"key":"10.1016\/j.camwa.2006.04.009_bib24","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1016\/j.enganabound.2004.05.006","article-title":"On approximate cardinal preconditioning methods for radial functions","volume":"29","author":"Brown","year":"2005","journal-title":"Eng. Anal. Bound. Elem."},{"key":"10.1016\/j.camwa.2006.04.009_bib25","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1016\/j.enganabound.2005.07.003","article-title":"Improved numerical solver for Kansa's method based on affine space decomposition","volume":"29","author":"Ling","year":"2005","journal-title":"Eng. Anal. Bound. Elem."}],"container-title":["Computers & Mathematics with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122106000794?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122106000794?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T00:59:43Z","timestamp":1587085183000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0898122106000794"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4]]},"references-count":25,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2006,4]]}},"alternative-id":["S0898122106000794"],"URL":"https:\/\/doi.org\/10.1016\/j.camwa.2006.04.009","relation":{},"ISSN":["0898-1221"],"issn-type":[{"value":"0898-1221","type":"print"}],"subject":[],"published":{"date-parts":[[2006,4]]}}}