Abstract
Painlevé II equation is one of the six second-order ordinary differential equations namely Painlevé equations. This paper presented the numerical solution for Painlevé equation II via a new iterative method called Daftardar–Gejji and Jafari method (DJM). Comparison of the results obtained by DJM with those obtained by other methods such as optimal homotopy asymptotic method (OHAM), homotopy perturbation method (HPM), Sinc-collocation method, Chebyshev series method (CSM) and variational iterative method (VIM), revealed the effectiveness of the method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bhalekar S, Daftardar-Gejji V (2008) New iterative method: application to partial differential equations. Appl Math Comput 203(2):778–783
Bhalekar S, Daftardar-Gejji V (2011) Convergence of the new iterative method. Int J Differ Equ 2011. https://doi.org/10.1155/2011/989065
Bhalekar S, Daftardar-Gejji V (2012). Solving fractional-order logistic equation using a new iterative method. Int J Differ Equ 2012. https://doi.org/10.1155/2012/975829
Daftardar-Gejji V, Jafari H (2006) An iterative method for solving nonlinear functional equation. J Math Anal Appl 316(2):753–763
Daftardar-Gejji V, Bhalekar S (2010) Solving fractional boundary value problems with Dirichlet boundary condition using a new iterative method. Comput Math Appl 59:1801–1809
Dastidar DG, Majumdar SK (1972) The solution of Painlevé equations in Chebishev series. FC Auluk, FNA 4(2):155–160
Hemeda AA (2013) New iterative method: an application for solving fractional physical differential equations. Abstr Appl Anal 2013. https://doi.org/10.1155/2013/617010
Hesameddini E, Peyrovi A (2010) Homotopy perturbation method for second Painlevé equation and comparisons with analytic continuation extension and Chebishev series method. Int Math Forum 5(13):629–637
Mabood F, Khan WA, Ismail AI, Hashim I (2015) Series solution for Painlevé equation II. Walailak J Sci Technol 12(10):941–947
Majeed A-J (2014) A reliable iterative method for solving the epidemic model and the prey and predator problems. Int J Basic Appl Sci 3(4):441–450
Saadatmandi A (2012) Numerical study of second Painlevé equation. Commun Numer Anal 2012. https://doi.org/10.5899/2012/cna-00157
Yaseen M, Samraiz M, Naheed S (2013) Exact solution of Laplace equation by DJ method. Results Phys 3:38–40
Acknowledgments
Special thanks and appreciation to Research Management Centre, Universiti Teknologi MARA (UiTM) Malaysia for the research grants and for funding through this research project (File No: 600-RMI/IRAGS 5/3 (18/2015)).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Selamat, M.S., Latif, B., Aziz, N.A.A., Yahya, F. (2018). Numerical Solution of Painlevé Equation II via Daftardar–Gejji and Jafari Method. In: Yacob, N., Mohd Noor, N., Mohd Yunus, N., Lob Yussof, R., Zakaria, S. (eds) Regional Conference on Science, Technology and Social Sciences (RCSTSS 2016) . Springer, Singapore. https://doi.org/10.1007/978-981-13-0074-5_89
Download citation
DOI: https://doi.org/10.1007/978-981-13-0074-5_89
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-0073-8
Online ISBN: 978-981-13-0074-5
eBook Packages: Business and ManagementBusiness and Management (R0)