Collocation methods for integral fractional Laplacian and fractional PDEs based on radial basis functions

Qiao Zhuang, Alfa Heryudono, Fanhai Zeng and Zhongqiang Zhang

Applied Mathematics and Computation, 2024, vol. 469, issue C

Abstract: We consider collocation methods for fractional elliptic equations with the integral fractional Laplacian on general bounded domains using radial basis functions (RBFs). Leveraging the Hankel transform, we develop highly efficient numerical techniques for the integral fractional Laplacian of RBFs. Furthermore, we devise a collocation formulation toward practical applications that facilitates the use of a relatively large number of collocation points while maintaining smaller condition numbers compared to existing formulations. In addition to our focus on Matern RBFs, the proposed method is applicable to a broad class of positive definite RBFs with smooth Fourier transformations. We demonstrate the effectiveness of our method in solving several problems in both smooth and non-smooth planar domains.

Keywords: Radial basis function; Collocation methods; Numerical Hankel transform; Extended domain methods (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:469:y:2024:i:c:s0096300324000201

DOI: 10.1016/j.amc.2024.128548

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