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A new development of sixth order accurate compact scheme for the Helmholtz equation

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Abstract

A standard sixth order compact finite difference scheme for two dimensional Helmholtz equation is further improved and a more accurate scheme is presented for the two dimensional Helmholtz equation which is also compact. The novel feature of the present scheme is that it is less sensitive to the associated wave number when compared with that for available sixth order schemes. Theoretical analysis is presented for the newly constructed scheme. The high accuracy of the proposed scheme is illustrated by comparing numerical solutions for solving the two dimensional Helmholtz equations using available sixth-order schemes and the present scheme.

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Acknowledgements

The authors sincerely thank the editor and anonymous referees for detailed and very helpful suggestions and comments which significantly improved the presentation of this paper. The research work to the first author is supported by SRM Institute of Science and Technology Kattankulathur, Tamil Nadu India. The authors also acknowledge the SERB, New Delhi, India towards computational facility through project file No. MTR/2017/000187. Discussions with Dr. Shuvam Sen is also acknowledged.

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  1. Research Institute, SRM Institute of Science & Technology, Kattankulathur, Kancheepuram, Tamil Nadu, 603 203, India

    Neelesh Kumar

  2. Research Institute & Department of Mathematics, SRM Institute of Science & Technology, Kattankulathur, Tamil Nadu, 603 203, India

    Ritesh Kumar Dubey

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  1. Neelesh Kumar
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  2. Ritesh Kumar Dubey
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Correspondence to Neelesh Kumar.

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This work was supported by the SRMIST, Tamil Nadu; and SERB New Delhi, India under Grant [MTR/2017/000187].

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Kumar, N., Dubey, R.K. A new development of sixth order accurate compact scheme for the Helmholtz equation. J. Appl. Math. Comput. 62, 637–662 (2020). https://doi.org/10.1007/s12190-019-01301-x

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