Scopus İndeksli Yayınlar Koleksiyonu

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

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Subject: search.filters.subject.Finite Difference Formulation

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 52
    Citation - Scopus: 57
    A Numerical Investigation of Caputo Time Fractional Allen-Cahn Equation Using Redefined Cubic B-Spline Functions
    (Springer, 2020) Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Khalid, Nauman
    We present a collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation to study the approximate solution of time fractional Allen-Cahn equation (ACE). We discretize the time fractional derivative of order alpha is an element of (0,1] by using finite forward difference formula and bring RCBS functions into action for spatial discretization. We find that the numerical scheme is of order O(h2+Delta t2-alpha) and unconditionally stable. We test the computational efficiency of the proposed method through some numerical examples subject to homogeneous/nonhomogeneous boundary constraints. The simulation results show a superior agreement with the exact solution as compared to those found in the literature.
  • Article
    Citation - WoS: 58
    Citation - Scopus: 61
    Solving Time Fractional Burgers' and Fisher's Equations Using Cubic B-Spline Approximation Method
    (Springer, 2020) Kamran, Mohsin; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Majeed, Abdul
    This article presents a numerical algorithm for solving time fractional Burgers' and Fisher's equations using cubic B-spline finite element method. The L1 formula with Caputo derivative is used to discretized the time fractional derivative, whereas the Crank-Nicolson scheme based on cubic B-spline functions is used to interpolate the solution curve along the spatial grid. The numerical scheme has been implemented on three test problems. The obtained results indicate that the proposed method is a good option for solving nonlinear fractional Burgers' and Fisher's equations. The error norms L2 and L infinity have been calculated to validate the efficiency and accuracy of the presented algorithm.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 28
    A Numerical Algorithm Based on Modified Extended B-Spline Functions for Solving Time-Fractional Diffusion Wave Equation Involving Reaction and Damping Terms
    (Springer, 2019) Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Khalid, Nauman
    In this study, we have proposed an efficient numerical algorithm based on third degree modified extended B-spline (EBS) functions for solving time-fractional diffusion wave equation with reaction and damping terms. The Caputo time-fractional derivative has been approximated by means of usual finite difference scheme and the modified EBS functions are used for spatial discretization. The stability analysis and derivation of theoretical convergence validates the authenticity and effectiveness of the proposed algorithm. The numerical experiments show that the computational outcomes are in line with the theoretical expectations. Moreover, the numerical results are proved to be better than other methods on the topic.