Single cell discretization of O(kh2 + h4) for the estimates of ${partial u}over{partial n}$ for the two‐space dimensional quasi‐linear parabolic equation

In this article, new stable two‐level explicit difference methods of O(kh² + h⁴) for the estimates of 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