Browsing by Author "Akram, Tayyaba"

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Citation Count: Akram, Tayyaba...et al. (2020). "A Numerical Approach of a Time Fractional Reaction-Diffusion Model with a Non-Singular Kernel", Symmetry-Basel, Vol. 12, No. 10.
A Numerical Approach of a Time Fractional Reaction-Diffusion Model with a Non-Singular Kernel
(2020) Akram, Tayyaba; Abbas, Muhammad; Ali, Ajmal; Iqbal, Azhar; Baleanu, Dumitru; 56389
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.
Citation Count: Akram, Tayyaba...et al. (2019). "Extended cubic B-splines in the numerical solution of time fractional telegraph equation", Advances in Difference Equations, Vol. 2019, No. 1.
Extended cubic B-splines in the numerical solution of time fractional telegraph equation
(Springer Open, 2019) Akram, Tayyaba; Abbas, Muhammad; İsmail, Ahmad İzani; Ali, Norhashidah Hj M.; Baleanu, Dumitru; 56389
A finite difference scheme based on extended cubic B-spline method for the solution of time fractional telegraph equation is presented and discussed. The Caputo fractional formula is used in the discretization of the time fractional derivative. A combination of the Caputo fractional derivative together with an extended cubic B-spline is utilized to obtain the computed solutions. The proposed scheme is shown to possess the unconditional stability property with second order convergence. Numerical results demonstrate the applicability, simplicity and the strength of the scheme in solving the time fractional telegraph equation with accuracies very close to the exact solutions.
Citation Count: Akram, Tayyaba...et al. (2020). "Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation", Symmetry-Basel, Vol. 12, No. 7.
Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation
(2020) Akram, Tayyaba; Abbas, Muhammad; Iqbal, Azhar; Baleanu, Dumitru; Asad, Jihad H.; 56389
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.