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

Yıl 2024, , 142 - 153, 16.12.2024

Roberto Cavoretto , Alessandra De Rossi , Domenico Mezzanotte

https://doi.org/10.33205/cma.1538581

Öz

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.

Anahtar Kelimeler

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

Destekleyen Kurum

ICSC - Centro Nazionale di Ricerca in High-Performance Computing, Big Data and Quantum Computing; INdAM Research group GNCS.

Teşekkür

RITA "Research ITalian network on Approximation"; UMI Group TAA "Approximation Theory and Applications"; SIMAI Activity Group ANA&A "Numerical and Analytical Approximation of Data and Functions with Applications".

Kaynakça

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