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Numerical simulation of space-fractional Helmholtz equation arising in seismic wave propagation, imaging and inversion

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Abstract

In this paper, a reliable numerical scheme, the q-fractional homotopy analysis transform method (q-FHATM), is proposed to examine the Helmholtz equation of fractional order arising in seismic wave propagation, imaging and inversion. Sufficient conditions for its convergence and error estimates are established. The q-FHATM provides a solution in a rapidly convergent series. Results for different fractional values of space derivatives are compared with the existing methods and discussed with the help of figures. A proper selection of parameters yields approximations identical to the exact solution. Parameter \(\hbar \) offers an expedient way of controlling the region of convergence of the solution. Test examples are provided to illustrate the accuracy and competency of the proposed scheme. The outcomes divulge that our scheme is attractive, user-friendly, reliable and highly effective.

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Acknowledgements

The authors are thankful to the reviewers and the editor for their valuable comments in improving the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Kurukshetra, 136 119, India

    Amit Prakash

  2. Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura, 281 406, India

    Manish Goyal & Shivangi Gupta

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  1. Amit Prakash
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  2. Manish Goyal
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  3. Shivangi Gupta
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Correspondence to Amit Prakash.

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Prakash, A., Goyal, M. & Gupta, S. Numerical simulation of space-fractional Helmholtz equation arising in seismic wave propagation, imaging and inversion. Pramana - J Phys 93, 28 (2019). https://doi.org/10.1007/s12043-019-1773-8

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  • DOI: https://doi.org/10.1007/s12043-019-1773-8

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