http://repository.iitr.ac.in/handle/123456789/9091
Title: | A new three-level implicit cubic spline method for the solution of 1D quasi-linear hyperbolic equations |
Authors: | Mohanty R.K. Jain, Manoj Kumar Singh S. |
Published in: | Computational Mathematics and Modeling |
Abstract: | In this paper, we study a new three-level implicit compact finite-difference discretization of O(k2 + k2h2 + h4), based on cubic spline approximation, for the solution of one-space dimensional second-order quasi-linear hyperbolic partial differential equations, where k > 0 and h > 0 are mesh sizes in time and space directions, respectively. We describe the complete derivation procedure of the method in detail and also discuss how our discretization is able to handle the wave equation in polar coordinates. The proposed method when applied to a linear telegraphic equation is also shown to be unconditionally stable. Some examples and their numerical results are provided to justify the usefulness of the proposed method. © 2013 Springer Science+Business Media New York. |
Citation: | Computational Mathematics and Modeling (2013), 24(3): 452-470 |
URI: | https://doi.org/10.1007/s10598-013-9190-1 http://repository.iitr.ac.in/handle/123456789/9091 |
Issue Date: | 2013 |
Keywords: | cubic spline approximation maximum absolute errors Quasi-linear hyperbolic equation telegraphic equation Van der Pol equation wave equation in polar coordinates |
ISSN: | 1046283X |
Author Scopus IDs: | 22938082300 56226587200 55793189851 |
Author Affiliations: | Mohanty, R.K., Department of Mathematics, University of Delhi, Delhi-110 007, India Jain, M.K., Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi-110 016, India Singh, S., Department of Mathematics, University of Delhi, Delhi-110 007, India |
Funding Details: | This research was supported by “The University of Delhi” under research grant No. D/011/23. |
Corresponding Author: | Mohanty, R. K.; Department of Mathematics, University of Delhi, Delhi-110 007, India; email: rmohanty@maths.du.ac.in |
Appears in Collections: | Journal Publications [HY] |
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