Solving the Linear Integral Equations Based on Radial Basis Function Interpolation | Zendy

Huaiqing Zhang | Zendy; Yu Chen | Zendy; Xin Nie | Zendy

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Solving the Linear Integral Equations Based on Radial Basis Function Interpolation

Author(s) -

Huaiqing Zhang,

Yu Chen,

Xin Nie

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/793582

Subject(s) - radial basis function , interpolation (computer graphics) , quadrature (astronomy) , integral equation , mathematics , basis function , collocation method , gauss , matrix (chemical analysis) , function (biology) , gaussian quadrature , nyström method , algorithm , mathematical analysis , computer science , differential equation , artificial intelligence , physics , materials science , artificial neural network , motion (physics) , ordinary differential equation , quantum mechanics , evolutionary biology , optics , composite material , biology

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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