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2014 Application of Radial Basis Function Method for Solving Nonlinear Integral Equations
Huaiqing Zhang, Yu Chen, Chunxian Guo, Zhihong Fu
J. Appl. Math. 2014: 1-8 (2014). DOI: 10.1155/2014/381908

Abstract

The radial basis function (RBF) method, especially the multiquadric (MQ) function, was proposed for one- and two-dimensional nonlinear integral equations. 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’s 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.

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Huaiqing Zhang. Yu Chen. Chunxian Guo. Zhihong Fu. "Application of Radial Basis Function Method for Solving Nonlinear Integral Equations." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/381908

Information

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

zbMATH: 07131561
MathSciNet: MR3275767
Digital Object Identifier: 10.1155/2014/381908

Rights: Copyright © 2014 Hindawi

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