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Browsing by Author "Khalid, Nauman"

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    Citation Count: Khalid, Nauman...et al. (2019). "A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms", Advances in Difference Equations, Vol. 2019, No. 1.
    A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms
    (Springer Open, 2019) Khalid, Nauman; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
    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.
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    Citation Count: Khalid, Nauman...et al. (2020). "A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions", Advances in Difference Equations, Vol. 2020, No. 1.
    A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions
    (2020) Khalid, Nauman; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
    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.