Homotopy analysis method with a non-homogeneous term in the auxiliary linear operator

► This paper modifies the normal homotopy analysis method. ► The method proposed shows faster convergence. ► This method may reduce computational cost and effort. We demonstrate the efficiency of a modification of the normal homotopy analysis method (HAM) proposed by Liao [2] by including a non-homo...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2012-10, Vol.17 (10), p.3776-3787
Main Authors: Shukla, Anant Kant, Ramamohan, T.R., Srinivas, S.
Format: Article
Language:English
Subjects:
Computer simulation
Convergence
Convergence theorem
Further generalization
Ham
Homotopy analysis method
Linear operators
Mathematical models
Non-homogeneous auxiliary linear operator
Nonlinearity
Theorems
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Summary:► This paper modifies the normal homotopy analysis method. ► The method proposed shows faster convergence. ► This method may reduce computational cost and effort. We demonstrate the efficiency of a modification of the normal homotopy analysis method (HAM) proposed by Liao [2] by including a non-homogeneous term in the auxiliary linear operator (this can be considered as a special case of “further generalization” of HAM given by Liao in [2]). We then apply the modified method to a few examples. It is observed that including a non-homogeneous term gives faster convergence in comparison to normal HAM. We also prove a convergence theorem, which shows that our technique yields the convergent solution.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2012.02.016