Recently, several numerical methods have been developed for solving time-fractional differential equations not only on rectangular computationaldomains but also on convex and non-convexnon-rectangular computational ...
详细信息
Recently, several numerical methods have been developed for solving time-fractional differential equations not only on rectangular computationaldomains but also on convex and non-convexnon-rectangular computational geometries. On the other hand, due to the existence of integrals in the definition of space-fractional operators, there are few numerical schemes for solving space-fractional differential equations on irregular regions. In this paper, we develop a novel numerical solution based on the machine learning technique and a generalized moving least squares approximation for two-dimensional fractional PDEs on irregular domains. The scheme is constructed on the monomials, and this is the strength of this technique. Moreover, it will be used to approximate the space derivatives on convex and non-convexnon-rectangular computationaldomains. The numerical results are extended to solve the fractional Bloch-Torrey equation, fractional Gray-Scott equation, and fractional Fitzhugh-Nagumo equation. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
暂无评论