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2014 Solving the Linear Integral Equations Based on Radial Basis Function Interpolation
Huaiqing Zhang, Yu Chen, Xin Nie
J. Appl. Math. 2014: 1-8 (2014). DOI: 10.1155/2014/793582


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.


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Huaiqing Zhang. Yu Chen. Xin Nie. "Solving the Linear Integral Equations Based on Radial Basis Function Interpolation." J. Appl. Math. 2014 1 - 8, 2014.


Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131869
MathSciNet: MR3219433
Digital Object Identifier: 10.1155/2014/793582

Rights: Copyright © 2014 Hindawi


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