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.

翻译：本文提出了一种新的自适应双曲交叉空间映射雅可比方法，用于求解无界区域中的多维时空积分微分方程。通过为定义在双曲交叉空间中的稀疏映射雅可比谱展开设计自适应技术，我们提出的AHMJ方法能够以较少的基函数数量高效求解各类时空积分微分方程，例如反常扩散模型。我们对AHMJ方法的分析给出了求解一类时空积分微分方程的统一上界误差，从而实现有效的误差控制。