Positivity preserving interpolation by using rational quartic spline

Noor Adilla Harim; Samsul Ariffin Abdul Karim; Mahmod Othman; Azizan Saaban; Abdul Ghaffar; Kottakkaran Sooppy Nisar; Dumitru Baleanu; Noor Adilla Harim; Samsul Ariffin Abdul Karim; Mahmod Othman; Azizan Saaban; Abdul Ghaffar; Kottakkaran Sooppy Nisar; Dumitru Baleanu

doi:10.3934/math.2020244

AIMS Mathematics

2020, Volume 5, Issue 4: 3762-3782. doi: 10.3934/math.2020244

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Research article

Positivity preserving interpolation by using rational quartic spline

1.
Fundamental and Applied Science Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610 Seri Iskandar, Perak DR, Malaysia
2.
Fundamental and Applied Sciences Department and Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610 Seri Iskandar, Perak DR
3.
School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah, Malaysia
4.
Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
5.
Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
6.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
7.
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
8.
Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
9.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan

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.
- Positivity,
- rational quartic spline,
- shape-preserving,
- C¹ continuity,
- positive data
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

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Abstract

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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