An adaptive radial basis function approach for efficiently solving multidimensional spatiotemporal integrodifferential equations
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908941596753920 |
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| author | Xia, Mingtao Shen, Qijing |
| author_facet | Xia, Mingtao Shen, Qijing |
| contents | In this work, we propose an adaptive radial basis function (RBF) approach for the efficient solution of multidimensional spatiotemporal integrodifferential equations. Our approach can automatically adjust the shape of RBFs and provide an easy-to-implement and mesh-free approach for solving spatiotemporal equations. Specifically, we analyze how the proposed method mitigates the curse of dimensionality by adaptively adjusting the scales and centers of the radial basis functions when the solution is spatially anisotropic. Through a range of numerical examples, we demonstrate the effectiveness of our approach for solving multidimensional spatiotemporal integrodifferential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05276 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An adaptive radial basis function approach for efficiently solving multidimensional spatiotemporal integrodifferential equations Xia, Mingtao Shen, Qijing Numerical Analysis 65M15, 65M70, 65N99 In this work, we propose an adaptive radial basis function (RBF) approach for the efficient solution of multidimensional spatiotemporal integrodifferential equations. Our approach can automatically adjust the shape of RBFs and provide an easy-to-implement and mesh-free approach for solving spatiotemporal equations. Specifically, we analyze how the proposed method mitigates the curse of dimensionality by adaptively adjusting the scales and centers of the radial basis functions when the solution is spatially anisotropic. Through a range of numerical examples, we demonstrate the effectiveness of our approach for solving multidimensional spatiotemporal integrodifferential equations. |
| title | An adaptive radial basis function approach for efficiently solving multidimensional spatiotemporal integrodifferential equations |
| topic | Numerical Analysis 65M15, 65M70, 65N99 |
| url | https://arxiv.org/abs/2604.05276 |