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Browsing by Author "Iqbal, M. S."

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    Article
    A novel time efficient structure-preserving splitting method for the solution of two-dimensional reaction-diffusion systems
    (2020) Baleanu, Dumitru; Korkmaz, Alper; Rafiq, M.; Baleanu, Dumitru; Alshomrani, Ali Sale; Rehman, M. A.; Iqbal, M. S.; 56389
    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.
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    Article
    Analytical optical soliton solutions of the Schrodinger-Poisson dynamical system
    (2021) Baleanu, Dumitru; Seadawy, Aly R; Baber, M. Z.; Husain, S.; Iqbal, M. S.; Rizvi, S. T. R.; Baleanu, Dumitru; 56389
    The article studies the exact traveling wave solutions to the Schrodinger-Poisson system which has applications in gravity's role of quantum state and approximate the coupling between quantum mechanics with gravitation. Diverse exact solutions in hyperbolic, trigonometric and plane wave forms are obtain using two norms of integration. For this sake modified extended direct algebraic (MEDA) and (G'/G)-expansion techniques are used. The 3D plots and their corresponding contour graphs are also depicted. The constraints conditions for the exact of solutions are also emerged during the derivation of solution.