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A New Numerical Method Based on Non-Polynomial Spline in Tension Approximations for 1D Quasilinear Hyperbolic Equations on a Variable Mesh

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Abstract

In this paper, we derive a new three level implicit method of order two in time and three in space, based on spline in tension approximation for the numerical solution of one space dimensional quasi-linear second order hyperbolic partial differential equation on a variable mesh. We also study application of the proposed method to wave equation in polar coordinates. High order approximation at first time level is briefly discussed which is applicable to solve problems both on uniform and non-uniform mesh. Numerical results are given to illustrate the usefulness of the proposed method.

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Acknowledgments

The authors thank the anonymous reviewers for their valuable suggestions, which substantially improved the standard of the paper.

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Author notes

  1. Ravindra Kumar

    Present address: Department of Mathematics, Rajdhani College, University of Delhi, New Delhi, 110015, India

Authors and Affiliations

  1. Department of Applied Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi, 110021, India

    Ranjan Kumar Mohanty

  2. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110007, India

    Ravindra Kumar

Authors
  1. Ranjan Kumar Mohanty
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  2. Ravindra Kumar
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Correspondence to Ranjan Kumar Mohanty.

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Mohanty, R.K., Kumar, R. A New Numerical Method Based on Non-Polynomial Spline in Tension Approximations for 1D Quasilinear Hyperbolic Equations on a Variable Mesh. Differ Equ Dyn Syst 25, 207–222 (2017). https://doi.org/10.1007/s12591-015-0261-y

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  • DOI: https://doi.org/10.1007/s12591-015-0261-y

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