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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/9150
Title: Fourth-order approximations at first time level, linear stability analysis and the numerical solution of multidimensional second-order nonlinear hyperbolic equations in polar coordinates
Authors: Mohanty R.K.
Jain, Manoj Kumar
George K.
Published in: Journal of Computational and Applied Mathematics
Abstract: In this article, three-level implicit difference schemes of O(k4 + k2h2 + h4) where k>0, k>0 are grid sizes in time and space coordinates, respectively, are proposed for the numerical solution of one, two and three space-dimensional nonlinear wave equations in polar coordiantes subject to appropriate initial and Dirichlet boundary conditions. We also discuss fourth-order approximation at first time level for more general case. We also obtain the stability range of the difference scheme when applied to a test equation: utt = urr + α/rur - α/r2 u + g(r,t), α = 1 and 2. Numerical examples are provided to demonstrate the required order of convergence of the methods. © 1998 Elsevier Science B.V. All rights reserved.
Citation: Journal of Computational and Applied Mathematics (1998), 93(1): 1-12
URI: https://doi.org/10.1016/S0377-0427(98)00054-5
http://repository.iitr.ac.in/handle/123456789/9150
Issue Date: 1998
Publisher: Elsevier
ISSN: 3770427
Author Scopus IDs: 22938082300
56226587200
7202340971
Author Affiliations: Mohanty, R.K., Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India
Jain, M.K., Department of Mathematics, University of Mauritius, Reduit, Mauritius
George, K., Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India
Corresponding Author: Mohanty, R.K.; Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India; email: csec@doe.ernet.in
Appears in Collections:Journal Publications [HY]

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