Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Ahmed, NaumanPublisher: search.filters.publisher.Springer

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  • Article
    Citation - WoS: 12
    Citation - Scopus: 13
    A Novel Time Efficient Structure-Preserving Splitting Method for the Solution of Two-Dimensional Reaction-Diffusion Systems
    (Springer, 2020) Korkmaz, Alper; Rafiq, M.; Baleanu, Dumitru; Alshomrani, Ali Saleh; Rehman, M. A.; Iqbal, M. S.; Ahmed, Nauman
    In this article, the first part is concerned with the important questions related to the existence and uniqueness of solutions for nonlinear reaction-diffusion systems. Secondly, an efficient positivity-preserving operator splitting nonstandard finite difference scheme (NSFD) is designed for such a class of systems. The presented formulation is unconditionally stable as well as implicit in nature and even time efficient. The proposed NSFD operator splitting technique also preserves all the important properties possessed by continuous systems like positivity, convergence to the fixed points of the system, and boundedness. The proposed algorithm is implicit in nature but more efficient in time than the extensively used Euler method.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 14
    Positive Explicit and Implicit Computational Techniques for Reaction-Diffusion Epidemic Model of Dengue Disease Dynamics
    (Springer, 2020) Malik, Muhammad Rafiq; Baleanu, Dumitru; Alshomrani, Ali Saleh; Rehman, Muhammad Aziz-ur; Ahmed, Nauman; Rafiq, Muhammad
    The aim of this work is to develop a novel explicit unconditionally positivity preserving finite difference (FD) scheme and an implicit positive FD scheme for the numerical solution of dengue epidemic reaction-diffusion model with incubation period of virus. The proposed schemes are unconditionally stable and preserve all the essential properties of the solution of the dengue reaction diffusion model. This proposed FD schemes are unconditionally dynamically consistent with positivity property and converge to the true equilibrium points of dengue epidemic reaction diffusion system. Comparison of the proposed scheme with the well-known existing techniques is also presented. The time efficiency of both the proposed schemes is also compared, with the two widely used techniques.