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On comparison of series and numerical solutions for second Painlevé equation
Author(s) -
Ellahi R.,
Abbasbandy S.,
Hayat T.,
Zeeshan A.
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20475
Subject(s) - adomian decomposition method , mathematics , homotopy analysis method , homotopy perturbation method , legendre polynomials , series (stratigraphy) , analytic continuation , continuation , taylor series , mathematical analysis , decomposition method (queueing theory) , partial differential equation , homotopy , pure mathematics , paleontology , discrete mathematics , computer science , biology , programming language
Abstract This attempt presents the series solution of second Painlevé equation by homotopy analysis method (HAM). Comparison of HAM solution is provided with that of the Adomian decomposition method (ADM), homotopy perturbation method (HPM), analytic continuation method, and Legendre Tau method. It is revealed that there is very good agreement between the analytic continuation and HAM solutions when compared with ADM, HPM, and Legendre Tau solutions. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010