Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Ghaffar, AbdulScopus Q: search.filters.scopusQuartile.Q1

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  • Article
    Citation - WoS: 23
    Citation - Scopus: 31
    Solutions of Bvps Arising in Hydrodynamic and Magnetohydro-Dynamic Stability Theory Using Polynomial and Non-Polynomial Splines
    (Elsevier, 2021) Ghaffar, Abdul; Naeem, M. Nawaz; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Khalid, Aasma
    This paper describes the exceptionally precise results of 6th-order and 8th-order nonlinear boundary-value problems(BVPs). Cubic-Nonpolynomial spline(CNPS) and Cubic-polynomial spline(CNPS) are utilized to solve such types of BVPs. We develop the class of numerical techniques for a particular selection of the factors that are associated with nonpolynomial and polynomial splines. Using the developed class of numerical techniques, the problem is reduced to a new system that consists of 2nd-order BVPs only. The end conditions associated with the BVPs are determined. For each problem, the results obtained by CNPS and CPS is compared with the exact solution. The absolute error(AE) for every iteration is calculated. To show that the suitable responses established by using CNPS and CPS have a higher level of preciseness, the absolute errors of the CNPS and CPS have been compared with different techniques such as DTM, ADM, Parametric septic splines, Variational-iteration method(VIM), Daftardar Jafari strategy, MDM, Cubic B-Spline, Homotopy method(HM), Quintic and Sextic B-spline and observed to be more accurate. Graphs that describe the graphical comparison of CNPS and CPS at n = 10 are also included in this paper. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 5
    A Shape-Preserving Variant of Lane-Riesenfeld Algorithm
    (Amer inst Mathematical Sciences-aims, 2021) Mustafa, Ghulam; Khan, Husna A.; Baleanu, Dumitru; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Ashraf, Pakeeza
    This paper introduces a family of shape-preserving binary approximating subdivision schemes by applying a shape-preserving variant on the Lane-Riesenfeld algorithm. Using the symbols of subdivision schemes, we determine convergence and smoothness, Holder continuity, and support size of the limit curves. Furthermore, these schemes produce monotonic and convex curves under the certain conditions imposed on the initial data.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 13
    Positivity Preserving Interpolation by Using Rational Quartic Spline
    (Amer inst Mathematical Sciences-aims, 2020) Karim, Samsul Ariffin Abdul; Othman, Mahmod; Saaban, Azizan; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Harim, Noor Adilla
    In this study, a new scheme for positivity preserving interpolation is proposed by using C-1 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.