Spectral method for the two-dimensional time distributed-order diffusion-wave equation on a semi-infinite domain

The time distributed-order diffusion-wave equation describes radial groundwater flow to or from a well. In the paper, an alternating direction implicit (ADI) Legendre-Laguerre spectral scheme is proposed for the two-dimensional time distributed-order diffusion wave equation on a semi-infinite domain. The Gauss quadrature formula has a higher computational accuracy than the Composite Trapezoid formula and Composite Simpson formula, which is presented to approximate the distributed order time derivative so that the considered equation is transformed into a multi-term fractional equation. Moreover, the transformed equation is solved by discretizing in space by the ADI Legendre-Laguerre spectral scheme to avoid introducing the artificial boundary and in time using the weighted and shifted Grunwald-Letnikov difference (WSGD) method. A stability and convergence analysis is performed for the numerical approximation. Some numerical results are illustrated to justify the theoretical analysis. (C) 2021 Elsevier B.V. All rights reserved.