Read Hermite- Birkhoff- Interpolation mit radialen Basisfunktionen in gewichteten Sobolew- Räumen mit Anwendungen auf partielle Differentialgleichungen. by Carsten Franke Online

Title : Hermite- Birkhoff- Interpolation mit radialen Basisfunktionen in gewichteten Sobolew- Räumen mit Anwendungen auf partielle Differentialgleichungen.
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ISBN : 3897123053
ISBN13 : 978-3897123052
Format Type : E-Book
Language : Deutsch
Publisher : Cuvillier 15 Oktober 1998
Number of Pages : 389 Pages
File Size : 883 KB
Status : Available For Download
Last checked : 21 Minutes ago!

Hermite- Birkhoff- Interpolation mit radialen Basisfunktionen in gewichteten Sobolew- Räumen mit Anwendungen auf partielle Differentialgleichungen. Reviews

  • Mathematiker in KB
    2019-03-20 08:23

    This PhD thesis was written by myself and thus I only allow myself to paste its abstract here:This thesis generalizes the well known theory of interpolation and approximation with Radial Basis Functions (RBFs) to the numerical solution of partial differential equations (PDEs) by collocation. For this purpose, a theory of weighted Sobolev spaces is developped. Questions about solvability, condition and error estimates of those collocations using certain RBFs are answered by reduction to interpolation problems using other RBFs. For example, collocation with RBFs outperforms finite element methods (FEMs) in the cases of high regular solutions or high space dimensions.Some of the main results of this thesis have been published before in two papers, which use a slightly different theoretical approach:- Carsten Franke and Robert Schaback. Convergence Orders of Meshless Collocation Methods using Radial Basis Functions. Advances in Computational Mathematics 8(4):381-399, June 1998.- Carsten Franke and Robert Schaback. Solving Partial Differential Equations by Collocation using Radial Basis Functions. Applied Mathematics and Computation 93(1):73-82, June 1998.MSC:35A40 Numerical approximation to solutions41A25 Rate of convergence, degree of approximation41A63 Multidimensional problems65N35 Spectral, collocation and related methods65R20 Integral equations