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An Investigation on Three Point Explicit Schemes and Induced Numerical Oscillations

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Abstract

Spurious induced oscillations have been one of the fundamental problem associated with numerical approximation of the solution of hyperbolic conservation laws. In this note, using notion of data dependent stability, generic three point schemes for scalar case are analysed to show that the induced oscillations depend on initial data too. Further, it is concluded that it is not possible to have an initial data independent, ’uniformly’ non-oscillatory three point fixed stencil scheme irrespective of its accuracy.

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Notes

  1. Sonic region is the one where characteristics speed \(f'(u)\) changes its sign.

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Authors and Affiliations

  1. Research Institute and Department of Mathematics, SRM University, Chennai, 603203, Tamil Nadu, India

    Ritesh Kumar Dubey & Sabana Parvin

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  1. Ritesh Kumar Dubey
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  2. Sabana Parvin
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Correspondence to Ritesh Kumar Dubey.

Additional information

Carried out work is supported through DST-SERB India project EMR/2016/000394.

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Dubey, R.K., Parvin, S. An Investigation on Three Point Explicit Schemes and Induced Numerical Oscillations. Differ Equ Dyn Syst 27, 83–90 (2019). https://doi.org/10.1007/s12591-017-0382-6

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  • DOI: https://doi.org/10.1007/s12591-017-0382-6

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