Least-Squares Residual Power Series Method for the Time-Fractional Differential Equations

Jianke Zhang, Zhirou Wei, Lifeng Li and Chang Zhou

Complexity, 2019, vol. 2019, 1-15

Abstract:

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.

Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/8503/2019/6159024.pdf (application/pdf)
http://downloads.hindawi.com/journals/8503/2019/6159024.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:6159024

DOI: 10.1155/2019/6159024

Access Statistics for this article

More articles in Complexity from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().