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Impact of Linear Operator on the Convergence of HAM Solution: a Modified Operator Approach

Part of: Basic methods in fluid mechanics Foundations, constitutive equations, rheology Acceleration of convergence

Published online by Cambridge University Press:  27 January 2016

S. T. Hussain ,
S. Nadeem  and
M. Qasim
S. T. Hussain*
Affiliation:
Department of Mechanical and Materials Engineering, Spencer Engineering Building, N6A 5B9, University of Western Ontario, London, Ontario, Canada Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
S. Nadeem
Affiliation:
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
M. Qasim
Affiliation:
Department of Mathematics, COMSATS Institute of Information Technology, Chak Shahzad, Islamabad, Pakistan
*
*Corresponding author. Email:sthqau@gmail.com (S. T. Hussain)
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Abstract.

The linear operator plays an important role in the computational process of Homotopy Analysis Method (HAM). In HAM frame any kind of linear operator can be chosen to develop a solution. Hence, it is easy to introduce the modified/physical parameter dependent linear operators. The effective use of these operators has been judged through solving fluid flow problems. Modification in linear operators affects the solution and improves the computational efficiency of HAM for larger values of parameters. The convergence rate of the solution is rapid and several times higher resulting in lesser computational time.

Keywords

Optimal homotopy analysis method (OHAM)modified operatorrapid convergencelarge physical parametersstretching surface

MSC classification

Secondary: 76A05: Non-Newtonian fluids 65B99: None of the above, but in this section 76M25: Other numerical methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 3 , June 2016 , pp. 499 - 516
Copyright
Copyright © Global-Science Press 2016 

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