{"title":"非线性问题的Kansa RBF方法","authors":"M. Jankowska, A. Karageorghis, Chingshyang Chen","doi":"10.2495/CMEM-V6-N6-1000-1007","DOIUrl":null,"url":null,"abstract":"We apply the Kansa–radial basis function (RBF) collocation method to two– dimensional nonlinear boundary value problems. The system of nonlinear equations resulting from the Kansa–RBF discretiza- tion is solved by directly applying a standard nonlinear solver. In a natural way, the value of the shape parameter in the RBFs employed in the approximation is included in the unknowns to be determined. The numerical results of some examples are presented and analysed.","PeriodicalId":22520,"journal":{"name":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","volume":"1 1","pages":"1000-1007"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"14","resultStr":"{\"title\":\"Kansa RBF method for nonlinear problems\",\"authors\":\"M. Jankowska, A. Karageorghis, Chingshyang Chen\",\"doi\":\"10.2495/CMEM-V6-N6-1000-1007\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We apply the Kansa–radial basis function (RBF) collocation method to two– dimensional nonlinear boundary value problems. The system of nonlinear equations resulting from the Kansa–RBF discretiza- tion is solved by directly applying a standard nonlinear solver. In a natural way, the value of the shape parameter in the RBFs employed in the approximation is included in the unknowns to be determined. The numerical results of some examples are presented and analysed.\",\"PeriodicalId\":22520,\"journal\":{\"name\":\"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS\",\"volume\":\"1 1\",\"pages\":\"1000-1007\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"14\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2495/CMEM-V6-N6-1000-1007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"THE INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS AND EXPERIMENTAL MEASUREMENTS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2495/CMEM-V6-N6-1000-1007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We apply the Kansa–radial basis function (RBF) collocation method to two– dimensional nonlinear boundary value problems. The system of nonlinear equations resulting from the Kansa–RBF discretiza- tion is solved by directly applying a standard nonlinear solver. In a natural way, the value of the shape parameter in the RBFs employed in the approximation is included in the unknowns to be determined. The numerical results of some examples are presented and analysed.
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