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Applicant:
Indian Institute of Technology (IIT) Patna 
Author:
Amit K. Verma and Sheerin Kayenat, , On the Convergence of Mickens’ type Nonstandard Finite Difference Schemes on Lane-Emden Type Equations, ,  
Corresponding Authors:
Amit K. Verma 
DOI #:
https://doi.org/10.1007/s10910-018-0880-y 
Title:
On the Convergence of Mickens’ type Nonstandard Finite Difference Schemes on Lane-Emden Type Equations 
Journal:
Journal of Mathematical Chemistry  
Year:
2018 
Volume:
56 
Page:
1667–1706. 
Keywords:
Non-standard finite difference schemes, · Boundary value problems, · Cylindrical ,· Spherical, · Singular, · Non-linear, · Non-local 
Abstract:
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) 
Entered by:
Venkata Dantham on 2020-08-04 
 
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