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] Department of Mathematics, Harbin Institute of Technology at Weihai, Shandong, 264209, China; [2] College of Mathematics and Computer Science, GuangDong Ocean University, Guangdong, 524088, China; [3] School of Mathematics, Harbin Institute of Technology, Heilongjiang, 150006, China

年份：2023

外文期刊名：SSRN

收录：EI(收录号：20240016000)

语种：英文

外文关键词：Computation theory - Differentiation (calculus) - Diffusion in liquids - Linear equations - Partial differential equations

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 arbitrary domain. Gauss-Legendre quadrature formula is applied to discrete distributed-order derivative integral. The piecewise parabolic fractional interpolation theory is established and with the help of it, 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 high express ability of neural network to construct the bases functions set on arbitrary domain, which significantly reduces the computational consumption. The bases constructed based on the neural network allows the selection of 12 bases numbers to achieve the approximation effect of 1000 ordinary bases numbers. 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 meshless numerical approach. ? 2023, The Authors. All rights reserved.