Research article

Positivity preserving interpolation by using rational quartic spline

  • Received: 19 November 2019 Accepted: 01 April 2020 Published: 20 April 2020
  • MSC : 65D05, 65D07, 65D10, 65D17, 65D18

  • In this study, a new scheme for positivity preserving interpolation is proposed by using C1 rational quartic spline of (quartic/quadratic) with three parameters. The sufficient condition for the positivity rational quartic interpolant is derived on one parameter meanwhile the other two are free parameters for shape modification. These conditions will guarantee to provide positive interpolating curve everywhere. We tested the proposed positive preserving scheme with four positive data and compared the results with other established schemes. Based on the graphical and numerical results, we found that the proposed scheme is better than existing schemes, since it has extra free parameter to control the positive interpolating curve.

    Citation: Noor Adilla Harim, Samsul Ariffin Abdul Karim, Mahmod Othman, Azizan Saaban, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Dumitru Baleanu. Positivity preserving interpolation by using rational quartic spline[J]. AIMS Mathematics, 2020, 5(4): 3762-3782. doi: 10.3934/math.2020244

    Related Papers:

  • In this study, a new scheme for positivity preserving interpolation is proposed by using C1 rational quartic spline of (quartic/quadratic) with three parameters. The sufficient condition for the positivity rational quartic interpolant is derived on one parameter meanwhile the other two are free parameters for shape modification. These conditions will guarantee to provide positive interpolating curve everywhere. We tested the proposed positive preserving scheme with four positive data and compared the results with other established schemes. Based on the graphical and numerical results, we found that the proposed scheme is better than existing schemes, since it has extra free parameter to control the positive interpolating curve.


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