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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/9184
Title: Linear stability analysis and fourth-order approximations at first time level for the two space dimensional mildly quasi-linear hyperbolic equations
Authors: Mohanty R.K.
Arora U.
Jain M.K.
Published in: Numerical Methods for Partial Differential Equations
Abstract: In 1996, Mohanty et al. [1] presented a fourth-order finite difference solution of a two space dimensional nonlinear hyperbolic equation with Dirichlet boundary conditions. In 1998, Mohanty et al. [2] discussed a fourth-order approximation at first time level for the numerical solution of the one space dimensional hyperbolic equation. In both the cases, they have discussed the stability analysis for the linear hyperbolic equation having first-order space derivative terms. Recently, Mohanty et al. [3] have developed fourth-order difference formulas for the three space dimensional quasi-linear hyperbolic equations and obtained fourth-order approximation at first time level. In this article, we extend our strategy for solving the two space dimensional quasi-linear hyperbolic equation. An operator splitting method for a linear hyperbolic equation having a time derivative term is proposed. Linear stability analysis and fourth-order approximation at first time level for the two space dimensional quasi-linear hyperbolic equation are also discussed. The results of the numerical experiments are compared with the exact solution. © 2001 John Wiley & Sons, Inc.
Citation: Numerical Methods for Partial Differential Equations (2001), 17(6): 607-618
URI: https://doi.org/10.1002/num.1029
http://repository.iitr.ac.in/handle/123456789/9184
Issue Date: 2001
Keywords: Damped wave equation
First time level
Operator splitting
Pade' approximation
Quasi-linear
Root mean square errors
ISSN: 0749159X
Author Scopus IDs: 22938082300
9637637300
56226587200
Author Affiliations: Mohanty, R.K., Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110 007, India, Dept. of Computing, Nottingham Trent University, Burlington St., Nottingham, NG1 4BU, United Kingdom
Arora, U., 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-110070, India
Corresponding Author: Mohanty, R.K.; Dept. of Computing, Nottingham Trent University, Burlington St., Nottingham, NG1 4BU, United Kingdom; email: rmohanty@edu.ac.in
Appears in Collections:Journal Publications [HY]

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