Long time numerical behaviors of fractional pantograph equations

作     者：Li, Dongfang Zhang, Chengjian 

作者机构：Huazhong Univ Sci & Technol Sch Math & Stat Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Hubei Key Lab Engn Modeling & Sci Comp Wuhan 430074 Peoples R China 

出 版 物：《MATHEMATICS AND COMPUTERS IN SIMULATION》 (系统模拟中的数学与计算机)

年 卷 期：2020年第172卷第0期

页      面：244-257页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：NSFC  China [11971010  11771162] 

主　　题：Long time behavior Stability Fractional pantograph equations Fast algorithm 

摘      要：This paper is concerned with long time numerical behaviors of nonlinear fractional pantograph equations. The L1 method with the linear interpolation procedure is applied to solve these nonlinear problems. It is proved that the proposed numerical scheme can inherit the long time behavior of the underlying problems without any stepsize restrictions. After that, the fast evaluation is presented to speed up the calculation of the Caputo fractional derivative. Numerical examples are shown to confirm the theoretical results. Besides, several counter-examples are also given to show that not all the numerical methods can inherit the long time behavior of the underlying problems. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.