Solving the Linear Integral Equations Based on Radial Basis Function Interpolation
The radial basis function (RBF) method, especially the multiquadric (MQ) function, was introduced in solving linear integral equations. The procedure of MQ method includes that the unknown function was firstly expressed in linear combination forms of RBFs, then the integral equation was transformed...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/793582 |
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| author | Huaiqing Zhang Yu Chen Xin Nie |
| author_facet | Huaiqing Zhang Yu Chen Xin Nie |
| author_sort | Huaiqing Zhang |
| collection | DOAJ |
| description | The radial basis function (RBF) method, especially the multiquadric (MQ) function, was introduced in solving linear integral equations. The procedure of MQ method includes that the unknown function was firstly expressed in linear combination forms of RBFs, then the integral equation was transformed into collocation matrix of RBFs, and finally, solving the matrix equation and an approximation solution was obtained. Because of the superior interpolation performance of MQ, the method can acquire higher precision with fewer nodes and low computations which takes obvious advantages over thin plate splines (TPS) method. In implementation, two types of integration schemes as the Gauss quadrature formula and regional split technique were put forward. Numerical results showed that the MQ solution can achieve accuracy of 1E-5. So, the MQ method is suitable and promising for integral equations. |
| format | Article |
| id | doaj-art-5b0960b24ddc4386a71e96986190f7c9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5b0960b24ddc4386a71e96986190f7c92025-02-03T01:01:59ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/793582793582Solving the Linear Integral Equations Based on Radial Basis Function InterpolationHuaiqing Zhang0Yu Chen1Xin Nie2The State Key Laboratory of Transmission Equipment and System Safety and Electrical New Technology, Chongqing University, Chongqing 400044, ChinaThe State Key Laboratory of Transmission Equipment and System Safety and Electrical New Technology, Chongqing University, Chongqing 400044, ChinaThe State Key Laboratory of Transmission Equipment and System Safety and Electrical New Technology, Chongqing University, Chongqing 400044, ChinaThe radial basis function (RBF) method, especially the multiquadric (MQ) function, was introduced in solving linear integral equations. The procedure of MQ method includes that the unknown function was firstly expressed in linear combination forms of RBFs, then the integral equation was transformed into collocation matrix of RBFs, and finally, solving the matrix equation and an approximation solution was obtained. Because of the superior interpolation performance of MQ, the method can acquire higher precision with fewer nodes and low computations which takes obvious advantages over thin plate splines (TPS) method. In implementation, two types of integration schemes as the Gauss quadrature formula and regional split technique were put forward. Numerical results showed that the MQ solution can achieve accuracy of 1E-5. So, the MQ method is suitable and promising for integral equations.http://dx.doi.org/10.1155/2014/793582 |
| spellingShingle | Huaiqing Zhang Yu Chen Xin Nie Solving the Linear Integral Equations Based on Radial Basis Function Interpolation Journal of Applied Mathematics |
| title | Solving the Linear Integral Equations Based on Radial Basis Function Interpolation |
| title_full | Solving the Linear Integral Equations Based on Radial Basis Function Interpolation |
| title_fullStr | Solving the Linear Integral Equations Based on Radial Basis Function Interpolation |
| title_full_unstemmed | Solving the Linear Integral Equations Based on Radial Basis Function Interpolation |
| title_short | Solving the Linear Integral Equations Based on Radial Basis Function Interpolation |
| title_sort | solving the linear integral equations based on radial basis function interpolation |
| url | http://dx.doi.org/10.1155/2014/793582 |
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