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27.08.2024 | Original Article

Inverse Cauchy problem in the framework of an RBF-based meshless technique and trigonometric basis functions

verfasst von: Farzaneh Safari, Yanjun Duan

Erschienen in: Engineering with Computers | Ausgabe 6/2024

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Abstract

The purpose of this paper is to point out that it is possible to evaluate the approximation solution of elliptic Partial differential equations (PDEs) on regular and irregular domains where no boundary conditions are defined on some part of the boundary domain. In the presence of trigonometric basis functions (TBFs), the backward substitution method (BSM) coupled with the radial basis functions neural network (RBFNN) is implemented very easily and works well. As a result, the approximation of the boundary conditions and the approximation of the PDE inside the solution domain is separated. The particular solution with an ungiven part of the inhomogeneous boundary condition is completely analyzed by the RBFNN method, and the efficiency and accuracy of the developed algorithms are discussed.

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Metadaten
Titel
Inverse Cauchy problem in the framework of an RBF-based meshless technique and trigonometric basis functions
verfasst von
Farzaneh Safari
Yanjun Duan
Publikationsdatum
27.08.2024
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 6/2024
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-024-02049-0