On the use of high order difference methods for the system of one space second order nonlinear hyperbolic equations with variable coefficients |
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Authors: | R.K. Mohanty M.K. Jain Kochurani George |
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Affiliation: | 1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi-110007, India;2. Department of Mathematics, Faculty of Science, University of Mauritius, Reduit, Mauritius |
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Abstract: | Implicit difference schemes of O(k4 + k2h2 + h4), where k0, h 0 are grid sizes in time and space coordinates respectively, are developed for the efficient numerical integration of the system of one space second order nonlinear hyperbolic equations with variable coefficients subject to appropriate initial and Dirichlet boundary conditions. The proposed difference method for a scalar equation is applied for the wave equation in cylindrical and spherical symmetry. The numerical examples are given to illustrate the fourth order convergence of the methods. |
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Keywords: | Difference method Hyperbolic equation Linear stability Polar coordinates Nonlinear wave equation Maximum absolute errors |
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