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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
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
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:
Appears in Collections:Journal Publications [HY]

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