Scopus İndeksli Yayınlar Koleksiyonu

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

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20202

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

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Now showing 1 - 2 of 2
  • Article
    Citation - WoS: 16
    Citation - Scopus: 17
    Structure Preserving Computational Technique for Fractional Order Schnakenberg Model
    (Springer Heidelberg, 2020) Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-ur; Iqbal, Zafar
    The current article deals with the analysis and numerical solution of fractional order Schnakenberg (S-B) model. This model is a system of autocatalytic reactions by nature, which arises in many biological systems. This study is aiming at investigating the behavior of natural phenomena with a more realistic and practical approach. The solutions are obtained by applying the Grunwald-Letnikov (G-L) finite difference (FD) and the proposed G-L nonstandard finite difference (NSFD) computational schemes. The proposed formulation is explicit in nature, strongly structure preserving as well as it is independent of the time step size. One very important feature of our proposed scheme is that it preserves the positivity of the solution of continuous fractional order S-B model because the unknown variables involved in this system describe the chemical concentrations of different substances. The comparison of the proposed scheme with G-L FD method reflects the significance of the said method.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 9
    Structure Preserving Algorithms for Mathematical Model of Auto-Catalytic Glycolysis Chemical Reaction and Numerical Simulations
    (Springer Heidelberg, 2020) Ahmed, Nauman; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur; Khan, Ilyas; Ali, Mubasher; Nisar, Kottakkaran Sooppy
    This paper aims to develop positivity preserving splitting techniques for glycolysis reaction-diffusion chemical model. The positivity of state variables in the glycolysis model is an essential property that must be preserved for all choices of parameters. We propose two splitting methods that remain dynamically consistent with the continuous glycolysis reaction-diffusion model. The proposed methods converge to a true steady-state or fixed point under the given condition. On contrary to the classical operator splitting finite difference methods, we use nonstandard finite difference theory to propose a new class of operator splitting techniques.