Scopus İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Abbas, MuhammadWoS Q: search.filters.wosQuartile.Q2

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 40
    Citation - Scopus: 41
    Numerical Treatment of Time-Fractional Klein-Gordon Equation Using Redefined Extended Cubic B-Spline Functions
    (Frontiers Media Sa, 2020) Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Amin, Muhammad
    In this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein-Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order alpha is an element of (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme isO(h(2)+ Delta t(2-alpha)) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.
  • Article
    Citation - WoS: 34
    Citation - Scopus: 35
    A Numerical Approach of a Time Fractional Reaction-Diffusion Model With a Non-Singular Kernel
    (Mdpi, 2020) Abbas, Muhammad; Ali, Ajmal; Iqbal, Azhar; Baleanu, Dumitru; Akram, Tayyaba
    The time-fractional reaction-diffusion (TFRD) model has broad physical perspectives and theoretical interpretation, and its numerical techniques are of significant conceptual and applied importance. A numerical technique is constructed for the solution of the TFRD model with the non-singular kernel. The Caputo-Fabrizio operator is applied for the discretization of time levels while the extended cubic B-spline (ECBS) function is applied for the space direction. The ECBS function preserves geometrical invariability, convex hull and symmetry property. Unconditional stability and convergence analysis are also proved. The projected numerical method is tested on two numerical examples. The theoretical and numerical results demonstrate that the order of convergence of 2 in time and space directions.
  • Article
    Citation - WoS: 36
    Citation - Scopus: 37
    Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation
    (Mdpi, 2020) Abbas, Muhammad; Iqbal, Azhar; Baleanu, Dumitru; Asad, Jihad H.; Akram, Tayyaba
    The telegraph model describes that the current and voltage waves can be reflected on a wire, that symmetrical wave patterns can form along a line. A numerical study of these voltage and current waves on a transferral line has been proposed via a modified extended cubic B-spline (MECBS) method. The B-spline functions have the flexibility and high order accuracy to approximate the solutions. These functions also preserve the symmetrical property. The MECBS and Crank Nicolson technique are employed to find out the solution of the non-linear time fractional telegraph equation. The time direction is discretized in the Caputo sense while the space dimension is discretized by the modified extended cubic B-spline. The non-linearity in the equation is linearized by Taylor's series. The proposed algorithm is unconditionally stable and convergent. The numerical examples are displayed to verify the authenticity and implementation of the method.