Application of Radial Basis Function Method for Solving Nonlinear Integral Equations
Joint Authors
Guo, Chunxian
Fu, Zhihong
Chen, Yu
Zhang, Huaiqing
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-10-28
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Zhang, Huaiqing& Chen, Yu& Guo, Chunxian& Fu, Zhihong. 2014. Application of Radial Basis Function Method for Solving Nonlinear Integral Equations. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1039667
Modern Language Association (MLA)
Zhang, Huaiqing…[et al.]. Application of Radial Basis Function Method for Solving Nonlinear Integral Equations. Journal of Applied Mathematics No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1039667
American Medical Association (AMA)
Zhang, Huaiqing& Chen, Yu& Guo, Chunxian& Fu, Zhihong. Application of Radial Basis Function Method for Solving Nonlinear Integral Equations. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1039667
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1039667