Yazar "Alshaikh, Noorhan" seçeneğine göre listele

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    Öğe
    FRACTIONAL-ORDER NEWTON-RAPHSON METHOD FOR NONLINEAR EQUATION WITH CONVERGENCE AND STABILITY ANALYSES
    (World Scientific Publ Co Pte Ltd, 2023) Farman, Muhammad; Akgul, Ali; Alshaikh, Noorhan; Azeem, Muhammad; Asad, Jihad
    Fractional-order techniques have many applications in real-life problems nowadays. The utilization of fragmentary math in many parts of science and engineering is wide and somewhat recent. There are various types of subsidiaries that can be valuable in various issues. In this paper, we focus on the effect of this kind of fractional derivative in the search for roots of nonlinear equations and its dependence on the initial estimations. We will check the convergence and stability analyses of the fractional Newton-Raphson (FNR) method for the proposed definitions. We will apply fractional Riemann-Liouville and Caputo-derivatives in the standard Newton root-finding method for different examples and also verify convergence and stability for these problems. Finding a root is very important for nonlinear equations which are used to solve chemical, biological, and engineering problems.
  • [ X ]
    Öğe
    NON-POLYNOMIAL CUBIC SPLINE METHOD USED TO FATHOM SINE GORDON EQUATIONS IN 3+1 DIMENSIONS
    (Vinca Inst Nuclear Sci, 2023) Sattar, Rabia; Ahmad, Muhammad Ozair; Pervaiz, Anjum; Ahmed, Nauman; Akgul, Ali; Abdullaev, Sherzod; Alshaikh, Noorhan
    This study contains an algorithmic solution of the Sine Gordon equation in three space and time dimensional problems. For discretization, the central difference formula is used for the time variable. In contrast, space variable x, y, and z are discretized using the non-polynominal cubic spline functions for each. The proposed scheme brings the accuracy of order O(h(2) + k(2) + sigma(2) + iota(2)h(2) + iota(2)k(2) + iota(2)sigma(2)) by electing suitable parametric values. The paper also discussed the truncation error of the proposed method and obtained the stability analysis. Numerical problems are elucidated by this method and compared to results taken from the literature.