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Chen, C. S.; Karageorghis, Andreas; Amuzu, Lionel

Kansa RBF collocation method with auxiliary boundary centres for high order BVPs. (English) Zbl 1478.65135

J. Comput. Appl. Math. 398, Article ID 113680, 17 p. (2021).
Summary: In this study we apply a Kansa-radial basis function (RBF) collocation method to 2D and 3D boundary value problems (BVPs) governed by high order partial differential equations (PDEs) of order \(2\mathcal{N}\) where \(\mathcal{N}\in\mathbb{N}\), \(\mathcal{N}\geq 3\). As in such problems there are \(\mathcal{N}\) boundary conditions (BCs), \(\mathcal{N}\) distinct sets of boundary centres are needed. These could all be placed on the boundary with each set being different to the other or, alternatively, each set of boundary centres could be placed on a corresponding distinct curve surrounding the boundary of the problem. We apply these approaches to several 2D and 3D high order BVPs.

Cited in 3 Documents

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65N85 Fictitious domain methods for boundary value problems involving PDEs
35J30 Higher-order elliptic equations
65D12 Numerical radial basis function approximation

Keywords:

radial basis functions; Kansa method; high order partial differential equations; collocation; fictitious point method; multiquadrics

Software:

Matlab
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\textit{C. S. Chen} et al., J. Comput. Appl. Math. 398, Article ID 113680, 17 p. (2021; Zbl 1478.65135)
Full Text: DOI

References:

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