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Modified Shepard’s method by six-points local interpolant

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Abstract

In this paper, we present an improvement of the Hexagonal Shepard method which uses functional and first order derivative data. More in details, we use six-point basis functions in combination with the modified local interpolant on six-points. The resulting operator reproduces polynomials up to degree 3 and has quartic approximation order. Several numerical results show the good accuracy of approximation of the proposed operator.

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Acknowledgements

The authors are very grateful to the referees for their detailed and valuable comments which helped to greatly improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Ibn Tofail University, Kenitra, Morocco

    Otheman Nouisser & Benaissa Zerroudi

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  1. Otheman Nouisser
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  2. Benaissa Zerroudi
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Correspondence to Benaissa Zerroudi.

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Nouisser, O., Zerroudi, B. Modified Shepard’s method by six-points local interpolant. J. Appl. Math. Comput. 65, 651–667 (2021). https://doi.org/10.1007/s12190-020-01409-5

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  • DOI: https://doi.org/10.1007/s12190-020-01409-5

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