文献类型：期刊文献

英文题名：A meshless approach based on fractional interpolation theory and improved neural network bases for solving non-smooth solution of 2D fractional reaction-diffusion equation with distributed order

作者：Li, Lin[1];Chen, Zhong[1];Du, Hong[2];Jiang, Wei[1];Zhang, Biao[3]

机构：[1]Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Shandong, Peoples R China;[2]GuangDong Ocean Univ, Coll Math & Comp Sci, Zhanjiang 524088, Guangdong, Peoples R China;[3]Harbin Inst Technol, Sch Math, Harbin 150006, Heilongjiang, Peoples R China

年份：2024

卷号：138

外文期刊名：COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

收录：SCI-EXPANDED(收录号：WOS:001288092500001)、、EI(收录号：20243216804142)、Scopus(收录号：2-s2.0-85200147954)、WOS

基金：Authors thank two anonymous reviewers and editors very much for their valuable suggestions for improving our work. This work was supported by Guangdong Basic and Applied Basic Research Foundation, China (Grant No. 2022A1515010022) , GuangDong Ocean University, China (Grant No. R20050) .

语种：英文

外文关键词：Distributed order reaction-diffusion equation; Fractional interpolation theory; Improved neural network bases; Meshless method

外文摘要：The primary objective of this research paper is to present a novel and effective meshless numerical approach for solving the 2D time fractional reaction diffusion system with distributed order on an arbitrary domain. Gauss-Legendre quadrature formula is applied to discretize distributed- order derivative integral. We establish the piecewise parabolic fractional interpolation theory and with its assistance, the proposed approach can proficiently solve the non-smooth solutions of the equations and more accurately approximate the Caputo fractional derivative. This meshless method based on improved neural network bases combines the high accuracy approximation advantage and strong express ability of neural network to construct the basis functions set on arbitrary domains, which significantly reduces a computational consumption. The bases constructed based on the neural network allow the selection of 12 bases numbers to achieve an approximation equivalent to that of 1000 ordinary bases. The theoretical analyses of error and convergence order for the meshless approach are carried out. Numerical examples are implemented to validate the high precision and capability of the meshless numerical approach.