Adaptive Hyperbolic-cross-space Mapped Jacobi Method on Unbounded Domains with Applications to Solving Multidimensional Spatiotemporal Integrodifferential Equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917637376704512 |
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| author | Deng, Yunhong Shao, Sihong Mogilner, Alex Xia, Mingtao |
| author_facet | Deng, Yunhong Shao, Sihong Mogilner, Alex Xia, Mingtao |
| contents | In this paper, we develop a new adaptive hyperbolic-cross-space mapped Jacobi (AHMJ) method for solving multidimensional spatiotemporal integrodifferential equations in unbounded domains. By devising adaptive techniques for sparse mapped Jacobi spectral expansions defined in a hyperbolic cross space, our proposed AHMJ method can efficiently solve various spatiotemporal integrodifferential equations such as the anomalous diffusion model with reduced numbers of basis functions. Our analysis of the AHMJ method gives a uniform upper error bound for solving a class of spatiotemporal integrodifferential equations, leading to effective error control. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_07844 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive Hyperbolic-cross-space Mapped Jacobi Method on Unbounded Domains with Applications to Solving Multidimensional Spatiotemporal Integrodifferential Equations Deng, Yunhong Shao, Sihong Mogilner, Alex Xia, Mingtao Numerical Analysis In this paper, we develop a new adaptive hyperbolic-cross-space mapped Jacobi (AHMJ) method for solving multidimensional spatiotemporal integrodifferential equations in unbounded domains. By devising adaptive techniques for sparse mapped Jacobi spectral expansions defined in a hyperbolic cross space, our proposed AHMJ method can efficiently solve various spatiotemporal integrodifferential equations such as the anomalous diffusion model with reduced numbers of basis functions. Our analysis of the AHMJ method gives a uniform upper error bound for solving a class of spatiotemporal integrodifferential equations, leading to effective error control. |
| title | Adaptive Hyperbolic-cross-space Mapped Jacobi Method on Unbounded Domains with Applications to Solving Multidimensional Spatiotemporal Integrodifferential Equations |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.07844 |