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Volume 8, Issue 3
Impact of Linear Operator on the Convergence of HAM Solution: A Modified Operator Approach

S. T. Hussain, S. Nadeem & M. Qasim

DOI: 10.4208/aamm.2014.m809

Adv. Appl. Math. Mech., 8 (2016), pp. 499-516.

Published online: 2018-05

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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 less computational time.

  • Keywords

Optimal homotopy analysis method (OHAM), modified operator, rapid convergence, large physical parameters, stretching surface.

  • AMS Subject Headings

76-XX, 76A05, 65B99, 76M25

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{AAMM-8-499, author = {Hussain , S. T.Nadeem , S. and Qasim , M.}, title = {Impact of Linear Operator on the Convergence of HAM Solution: A Modified Operator Approach}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {3}, pages = {499--516}, 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 less computational time.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m809}, url = {http://global-sci.org/intro/article_detail/aamm/12100.html} }
TY - JOUR T1 - Impact of Linear Operator on the Convergence of HAM Solution: A Modified Operator Approach AU - Hussain , S. T. AU - Nadeem , S. AU - Qasim , M. JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 499 EP - 516 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m809 UR - https://global-sci.org/intro/article_detail/aamm/12100.html KW - Optimal homotopy analysis method (OHAM), modified operator, rapid convergence, large physical parameters, stretching surface. AB -

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 less computational time.

Hussain , S. T.Nadeem , S. and Qasim , M.. (2018). Impact of Linear Operator on the Convergence of HAM Solution: A Modified Operator Approach. Advances in Applied Mathematics and Mechanics. 8 (3). 499-516. doi:10.4208/aamm.2014.m809
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