A review of radial kernel methods for the resolution of Fredholm integral equations of the second kind

Abstract

The paper presents an overview of the existing literature concerning radial kernel meshfree methods for the numerical treatment of second-kind Fredholm integral equations. More in detail, it briefly recalls radial basis function (RBF) interpolation and cubature rules to properly describe numerical methods for two-dimensional linear Fredholm equations. The RBF approach allows us to consider the case when the involved functions are not known analytically, but only as vectors of scattered data samples. The described methods do not require any background mesh and, hence, are also independent on the geometry of the domain.

Keywords

• Radial basis functions
• Fredholm integral equations
• Meshfree methods
• Scattered data

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