Abstract
We present radial basis function (RBF) collocation methods for time-dependent space fractional problems on general bounded domains. Building on a recently developed approach for accurately computing the integral fractional Laplacian of any RBF, we design collocation schemes for fractional heat and Stokes equations using extended-domain techniques. In particular, we propose a numerical Leray projection method for fractional Stokes problems, where both the discrete projection operator and the collocation scheme are formulated on extended domains to handle complex domains. Numerical results demonstrate the effectiveness of the proposed methods in solving time-dependent nonlocal problems on complex domains.
Recommended Citation
Q. Zhuang et al., "Meshless Collocation Methods for Time-dependent Nonlocal Problems based on Radial Basis Functions," Electronic Research Archive, vol. 34, no. 2, pp. 1124 - 1156, AIMS Press, Jan 2026.
The definitive version is available at https://doi.org/10.3934/era.2026052
Department(s)
Mathematics and Statistics
Publication Status
Open Access
Keywords and Phrases
fractional heat equation; fractional Stokes equation; meshless collocation methods; radial basis functions; time-dependent nonlocal problems
International Standard Serial Number (ISSN)
2688-1594
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2026 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Jan 2026
