Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme(MDPI AG, 2020) Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Ghaffar, Abdul; Khan, Faheem; Ashraf, Pakeeza; Sehar, IremArticle Citation - WoS: 4Citation - Scopus: 5A 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, PakeezaThis 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: 1Citation - Scopus: 1A Divided Differences Based Medium To Analyze Smoothness of the Binary Bivariate Refinement Schemes(Springer, 2021) Mustafa, Ghulam; Baleanu, Dumitru; Chu, Yu-Ming; Hameed, RabiaIn this article, we present the continuity analysis of the 3D models produced by the tensor product scheme of (m + 1)-point binary refinement scheme. We use differences and divided differences of the bivariate refinement scheme to analyze its smoothness. The C-0, C(1 )and C-2 continuity of the general bivariate scheme is analyzed in our approach. This gives us some simple conditions in the form of arithmetic expressions and inequalities. These conditions require the mask and the complexity of the given refinement scheme to analyze its smoothness. Moreover, we perform several experiments by using these conditions on established schemes to verify the correctness of our approach. These experiments show that our results are easy to implement and are applicable for both interpolatory and approximating types of the schemes.Article Citation - WoS: 9Citation - Scopus: 15Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme(Mdpi, 2020) Ghaffar, Abdul; Baleanu, Dumitru; Sehar, Irem; Nisar, Kottakkaran Sooppy; Khan, Faheem; Ashraf, PakeezaIn this paper, we analyze shape-preserving behavior of a relaxed four-point binary interpolating subdivision scheme. These shape-preserving properties include positivity-preserving, monotonicity-preserving and convexity-preserving. We establish the conditions on the initial control points that allow the generation of shape-preserving limit curves by the four-point scheme. Some numerical examples are given to illustrate the graphical representation of shape-preserving properties of the relaxed scheme.Article Citation - WoS: 6Citation - Scopus: 14A Subdivision-Based Approach for Singularly Perturbed Boundary Value Problem(Springer, 2020) Ejaz, Syeda Tehmina; Baleanu, Dumitru; Ghaffar, Abdul; Nisar, Kottakkaran Sooppy; Mustafa, GhulamA numerical approach for solving second order singularly perturbed boundary value problems (SPBVPs) is introduced in this paper. This approach is based on the basis function of a 6-point interpolatory subdivision scheme. The numerical results along with the convergence, comparison and error estimation of the proposed approach are also presented.Article Citation - WoS: 5Citation - Scopus: 17A New Class of 2q-Point Nonstationary Subdivision Schemes and Their Applications(Mdpi, 2019) Bari, Mehwish; Ullah, Zafar; Iqbal, Mudassar; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Ghaffar, AbdulThe main objective of this study is to introduce a new class of 2q-point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs.Article Citation - WoS: 14Citation - Scopus: 26Construction and Application of Nine-Tic B-Spline Tensor Product Ss(Mdpi, 2019) Ghaffar, Abdul; Iqbal, Mudassar; Bari, Mehwish; Hussain, Sardar Muhammad; Manzoor, Raheela; Nisar, Kottakkaran Sooppy; Baleanu, DumitruIn this paper, we propose and analyze a tensor product of nine-tic B-spline subdivision scheme (SS) to reduce the execution time needed to compute the subdivision process of quad meshes. We discuss some essential features of the proposed SS such as continuity, polynomial generation, joint spectral radius, holder regularity and limit stencil. Some results of the SS using surface modeling with the help of computer programming are shown.