Least-squares residual power series method for the time-fractional differential equations
type: Item
instance of: scholarly article
title: Least-squares residual power series method for the time-fractional differential equations
zbMATH Open document ID: 1434.65215
DOI: 10.1155/2019/6159024
author: Jianke Zhang
author: Zhirou Wei
author: Lifeng Li
author: Chang Zhou
published in: Complexity
publication date: 2019-11-25T00:00:00Z
review text: Summary: In this study, an applicable and effective method, which is based on a least-squares residual power series method (LSRPSM), is proposed to solve the time-fractional differential equations. The least-squares residual power series method combines the residual power series method with the least-squares method. These calculations depend on the sense of Caputo. Firstly, using the classic residual power series method, the analytical solution can be solved. Secondly, the concept of fractional Wronskian is introduced, which is applied to validate the linear independence of the functions. Thirdly, a linear combination of the first few terms as an approximate solution is used, which contains unknown coefficients. Finally, the least-squares method is proposed to obtain the unknown coefficients. The approximate solutions are solved by the least-squares residual power series method with the fewer expansion terms than the classic residual power series method. The examples are shown in datum and images.The examples show that the new method has an accelerate convergence than the classic residual power series method.
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 7136330
zbMATH Keywords: least-squares residual power series method
zbMATH Keywords: time-fractional differential equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/6159024
OpenAlex ID: W2982441300
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Wikidata QID: Q126868233
description: scientific article; zbMATH DE number 7136330