 On the Optimal Auxiliary Linear Operator for the Spectral Homotopy Analysis Method Solution of Nonlinear Ordinary Differential EquationsS. S. Motsa Mathematical Problems in Engineering, 2014, vol. 2014, 1-15 Abstract: 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. Date: 2014 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:697845 DOI: 10.1155/2014/697845 Access Statistics for this article More articles in Mathematical Problems in Engineering from Hindawi |
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