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The unknown function was firstly interpolated by MQ functions and then by forming the nonlinear algebraic equations by the collocation method. Finally, the coefficients of RBFs were determined by Newton\u2019s iteration method and an approximate solution was obtained. In implementation, the Gauss quadrature formula was employed in one-dimensional and two-dimensional regular domain problems, while the quadrature background mesh technique originated in mesh-free methods was introduced for irregular situation. Due to the superior interpolation performance of MQ function, the method can acquire higher accuracy with fewer nodes, so it takes obvious advantage over the Gaussian RBF method which can be revealed from the numerical results.<\/jats:p>","DOI":"10.1155\/2014\/381908","type":"journal-article","created":{"date-parts":[[2014,10,28]],"date-time":"2014-10-28T21:37:39Z","timestamp":1414532259000},"page":"1-8","source":"Crossref","is-referenced-by-count":7,"title":["Application of Radial Basis Function Method for Solving Nonlinear Integral Equations"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-2631-4740","authenticated-orcid":true,"given":"Huaiqing","family":"Zhang","sequence":"first","affiliation":[{"name":"The State Key Laboratory of Transmission Equipment and System Safety and Electrical New Technology, Chongqing University, Chongqing 400044, China"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-4487-4186","authenticated-orcid":true,"given":"Yu","family":"Chen","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Transmission Equipment and System Safety and Electrical New Technology, Chongqing University, Chongqing 400044, China"}]},{"given":"Chunxian","family":"Guo","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Transmission Equipment and System Safety and Electrical New Technology, Chongqing University, Chongqing 400044, China"}]},{"given":"Zhihong","family":"Fu","sequence":"additional","affiliation":[{"name":"The State Key Laboratory of Transmission Equipment and System Safety and Electrical New Technology, Chongqing University, Chongqing 400044, China"}]}],"member":"98","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2012.09.010"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1137\/0724087"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2008.10.007"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.09.099"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2012.08.031"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2010.05.029"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.08.045"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2013.02.004"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2011.11.041"},{"key":"10","first-page":"1905","volume":"176","year":"1971","journal-title":"Journal of Geophysical Research"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(90)90272-L"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(92)90168-H"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/0898-1221(90)90271-K"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.05.034"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.10.004"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.03.038"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.11.013"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2007.02.063"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2009.11.053"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/793582"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620370205"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/0013-7944(94)00153-9"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/381908.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/381908.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/381908.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,28]],"date-time":"2016-07-28T22:01:19Z","timestamp":1469743279000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/381908\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":22,"alternative-id":["381908","381908"],"URL":"https:\/\/doi.org\/10.1155\/2014\/381908","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}