Journal
JOURNAL OF MATHEMATICAL CHEMISTRY
Volume 56, Issue 6, Pages 1667-1706Publisher
SPRINGER
DOI: 10.1007/s10910-018-0880-y
Keywords
Non-standard finite difference schemes; Boundary value problems; Cylindrical; Spherical; Singular; Non-linear; Non-local
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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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