Least-Squares Residual Power Series Method for the Time-Fractional Differential Equations
Joint Authors
Li, Lifeng
Wei, Zhirou
Zhou, Chang
Zhang, Jianke
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-10-30
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Zhang, Jianke& Wei, Zhirou& Li, Lifeng& Zhou, Chang. 2019. Least-Squares Residual Power Series Method for the Time-Fractional Differential Equations. Complexity،Vol. 2019, no. 2019, pp.1-15.
https://search.emarefa.net/detail/BIM-1132354
Modern Language Association (MLA)
Zhang, Jianke…[et al.]. Least-Squares Residual Power Series Method for the Time-Fractional Differential Equations. Complexity No. 2019 (2019), pp.1-15.
https://search.emarefa.net/detail/BIM-1132354
American Medical Association (AMA)
Zhang, Jianke& Wei, Zhirou& Li, Lifeng& Zhou, Chang. Least-Squares Residual Power Series Method for the Time-Fractional Differential Equations. Complexity. 2019. Vol. 2019, no. 2019, pp.1-15.
https://search.emarefa.net/detail/BIM-1132354
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1132354