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arXiv · 2404.07844

Adaptive Hyperbolic-cross-space Mapped Jacobi Method on Unbounded Domains with Applications to Solving Multidimensional Spatiotemporal Integrodifferential Equations

Yunhong Deng·Sihong Shao·Alex Mogilner·Mingtao Xia
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Abstract

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.

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Yunhong Deng, Sihong Shao, Alex Mogilner, Mingtao Xia. 2024-04-11. Adaptive Hyperbolic-cross-space Mapped Jacobi Method on Unbounded Domains with Applications to Solving Multidimensional Spatiotemporal Integrodifferential Equations. https://arxiv.org/abs/2404.07844

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