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Integrated multiquadric radial basis function approximation methods. (English) Zbl 1146.65327
Summary: Promising numerical results using once and twice integrated radial basis functions have been recently presented. In this work we investigate the integrated radial basis function (IRBF) concept in greater detail, connect to the existing RBF theory, and make conjectures about the properties of IRBF approximation methods. The IRBF methods are used to solve partial differential equations.

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65D15 Algorithms for approximation of functions
41A63 Multidimensional problems
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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