Efficient Adaptive Sparse Spectral Method for Solving Multidimensional Spatiotemporal Integrodifferential Equations in Unbounded Domains

The authors develop an adaptive hyperbolic-cross-space mapped Jacobi (AHMJ) method to efficiently solve multidimensional spatiotemporal integrodifferential equations in unbounded domains. The AHMJ method uses adaptive techniques for sparse mapped Jacobi spectral expansions defined in a hyperbolic cross space, allowing for effective solution of various spatiotemporal integrodifferential equations with reduced numbers of basis functions. The analysis provides a uniform upper error bound for solving a class of spatiotemporal integrodifferential equations, enabling effective error control.