On the Optimal Auxiliary Linear Operator for the Spectral Homotopy Analysis Method Solution of Nonlinear Ordinary Differential Equations
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-08-13
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
The purpose of this study is to identify the auxiliary linear operator that gives the best convergence and accuracy in the implementation of the spectral homotopy analysis method (SHAM) in the solution of nonlinear ordinary differential equations.
The auxiliary linear operator is an essential element of the homotopy analysis method (HAM) algorithm that strongly influences the convergence of the method.
In this work we introduce new procedures of defining the auxiliary linear operators and compare solutions generated using the new linear operators with solutions obtained using well-known linear operators.
The applicability and validity of the proposed linear operators is tested on four highly nonlinear ordinary differential equations with fluid mechanics applications that have recently been reported in the literature.
The results from the study reveal that the new linear operators give better results than the previously used linear operators.
The identification of the optimal linear operator will direct future research on further applications of HAM-based methods in solving complicated nonlinear differential equations.
American Psychological Association (APA)
Motsa, Sandile Sydney. 2014. On the Optimal Auxiliary Linear Operator for the Spectral Homotopy Analysis Method Solution of Nonlinear Ordinary Differential Equations. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-491477
Modern Language Association (MLA)
Motsa, Sandile Sydney. On the Optimal Auxiliary Linear Operator for the Spectral Homotopy Analysis Method Solution of Nonlinear Ordinary Differential Equations. Mathematical Problems in Engineering No. 2014 (2014), pp.1-15.
https://search.emarefa.net/detail/BIM-491477
American Medical Association (AMA)
Motsa, Sandile Sydney. On the Optimal Auxiliary Linear Operator for the Spectral Homotopy Analysis Method Solution of Nonlinear Ordinary Differential Equations. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-15.
https://search.emarefa.net/detail/BIM-491477
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-491477