Abstract
In this paper, we analyse Mickens’ type non-standard finite difference schemes (NSFD) and establish their convergence. We then apply these schemes on Lane Emden equations. The numerical results thus obtained are compared with existing analytical solutions or with solutions computed with standard finite difference (FD) schemes. NSFD and FD solutions and their errors have also been compared graphically and observed that the errors in NSFD tends to zero as step size tends to zero. The result shows that the NSFD behave qualitatively in the same way as the original equations. NSFD approximate solution near singular point efficiently where FD fails to do so (Buckmire in Numer Methods Partial Differ Equ 19:380–398, 2003).
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28 February 2019
In the original article, the analytical solution of Problem 9 is published incorrectly.
28 February 2019
In the original article, the analytical solution of Problem 9 is published incorrectly.
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Acknowledgements
We are thankful to Prof. R. E. Mickens and Ron Buckmire whose ideas are applied while constructing the schemes for all of the above problems. We are also thankful to anonymous reviewers for their valuable comments.
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Amit Kumar Verma: In the memory of my loving mother Late Shrimati Mithlesh Verma, a teacher by profession.
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Verma, A.K., Kayenat, S. On the convergence of Mickens’ type nonstandard finite difference schemes on Lane-Emden type equations. J Math Chem 56, 1667–1706 (2018). https://doi.org/10.1007/s10910-018-0880-y
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DOI: https://doi.org/10.1007/s10910-018-0880-y