Numerical solution of the two-dimensional Fredholm integral equations using Gaussian radial basis function

DOI10.1016/j.cam.2009.11.053zbMath1226.65105OpenAlexW2078914286MaRDI QIDQ719419

Amjad Alipanah, Shahrokh Esmaeili

Publication date: 10 October 2011

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.11.053

zbMATH Keywords

numerical examplesGaussianradial basis functionnonlinear Fredholm integral equationstwo-dimensional integral equationsLegendre-Gauss-Lobatto nodes

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Fredholm integral equations (45B05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Theory and applications of the multiquadric-biharmonic method. 20 years of discovery 1968-1988
• A numerical study of some radial basis function based solution methods for elliptic PDEs
• The discrete Galerkin method for nonlinear integral equations
• Strictly positive definite functions
• A survey of numerical methods for solving nonlinear integral equations
• Multiquadratic interpolation improved
• Integral equations. Theory and numerical treatment
• Analytic wavelets generated by radial functions
• A pseudospectral method for Hammerstein equations
• Numerical solution of the nonlinear Fredholm integral equations by positive definite functions
• An efficient numerical approximation for the linear class of mixed integral equations
• The Discrete Galerkin Method for Integral Equations
• Radial Basis Functions
• Spectral Methods
• The Numerical Solution of Fredholm integral Equations of the Second Kind
• Richardson extrapolation of iterated discrete Galerkin solution for two-dimensional Fredholm integral equations

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