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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/9238
Title: Single-cell discretization of O(kh2 + h4) for ∂u/∂n for three-space dimensional mildly quasi-linear parabolic equation
Authors: Mohanty R.K.
Kumar D.
Jain, Manoj Kumar
Published in: Numerical Methods for Partial Differential Equations
Abstract: In this article, using a single computational cell, we report some stable two-level explicit finite difference approximations of O(kh2 + h4) for ∂u/∂n for three-space dimensional quasi-linear parabolic equation, where h > 0 and k > 0 are mesh sizes in space and time directions, respectively. When grid lines are parallel to x-, y-, and z-coordinate axes, then ∂u/∂n at an internal grid point becomes ∂u/∂x, ∂u/∂y, and ∂u/∂z, respectively. The proposed methods are also applicable to the polar coordinates problems. The proposed methods have the simplicity in nature and use the same marching type of technique of solution. Stability analysis of a linear difference equation and computational efficiency of the methods are discussed. The results of numerical experiments are compared with exact solutions.
Citation: Numerical Methods for Partial Differential Equations (2003), 19(3): 327-342
URI: https://doi.org/10.1002/num.10050
http://repository.iitr.ac.in/handle/123456789/9238
Issue Date: 2003
Keywords: Alternating direct on implicit (ADI) method
Explicit scheme
Finite difference method
Quasi-linear parabolic equation
Single cell
Space derivatives
ISSN: 0749159X
Author Scopus IDs: 22938082300
57212687822
56226587200
Author Affiliations: Mohanty, R.K., Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110 007, India
Kumar, D., Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110 007, India
Jain, M.K., 4076, Sector-C, Pocket-4, Vasant Kunj, New Delhi-110 070, India
Corresponding Author: Mohanty, R.K.; Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110 007, India; email: rmohanty@du.ac.in
Appears in Collections:Journal Publications [HY]

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