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Single cell discretization of O ( kh 2 + h 4 ) for the estimates of ${\partial u}\over{\partial n}$ for the two‐space dimensional quasi‐linear parabolic equation
Author(s) -
Mohanty R. K.,
Jain M. K.,
Kumar Dinesh
Publication year - 2001
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.4
Subject(s) - mathematics , partial differential equation , cartesian coordinate system , discretization , partial derivative , space (punctuation) , parabolic partial differential equation , mathematical analysis , polar coordinate system , simplicity , finite difference , geometry , physics , quantum mechanics , philosophy , linguistics
In this article, new stable two‐level explicit difference methods of O ( kh 2 + h 4 ) for the estimates of ${\partial u}\over{\partial n}$ for the two‐space dimensional quasi‐linear parabolic equation are derived, where k > 0 and h > 0 are grid sizes in time and space directions, respectively. We use a single computational cell for the methods, which are applicable to the problems both in cartesian and polar coordinates. The proposed methods have the simplicity in nature and employ the same marching type technique of solution. Numerical results obtained by the proposed methods for several different problems were compared with the exact solutions. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 250–261, 2001