Numerical solution of second order Painlevé differential equation

Volume 21, Issue 2, pp 150--157 http://dx.doi.org/10.22436/jmcs.021.02.06
Publication Date: April 11, 2020 Submission Date: October 18, 2019 Revision Date: February 03, 2020 Accteptance Date: March 03, 2020

Authors

Hijaz Ahmad - Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan. Tufail A. Khan - Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan. Shao-Wen Yao - School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China.


Abstract

In this paper, the second order Painlevé differential equation is solved by variational iteration algorithm-I with an auxiliary parameter (VI-I with AP), how to optimally find the auxiliary parameter and Pade approximates for the numerical solution are explained. The effectiveness and suitability of the proposed method are shown by solving two types of second order Painlevé differential equation and the proposed method is compared with other methods to illustrate the accuracy and efficiency of the method.


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ISRP Style

Hijaz Ahmad, Tufail A. Khan, Shao-Wen Yao, Numerical solution of second order Painlevé differential equation, Journal of Mathematics and Computer Science, 21 (2020), no. 2, 150--157

AMA Style

Ahmad Hijaz, Khan Tufail A., Yao Shao-Wen, Numerical solution of second order Painlevé differential equation. J Math Comput SCI-JM. (2020); 21(2):150--157

Chicago/Turabian Style

Ahmad, Hijaz, Khan, Tufail A., Yao, Shao-Wen. "Numerical solution of second order Painlevé differential equation." Journal of Mathematics and Computer Science, 21, no. 2 (2020): 150--157


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