Browsing by Author "Amin, Muhammad"

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Citation Count: Amin, Muhammad...et al. (2019) "A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations", Advances in Difference Equations, Vol. 2019, No. 1.
A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations
(Springer, 2019) Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Ismail, Ahmad Izani Md.; Baleanu, Dumitru; 56389
The purpose of this article is to present a technique for the numerical solution of Caputo time fractional superdiffusion equation. The central difference approximation is used to discretize the time derivative, while non-polynomial quintic spline is employed as an interpolating function in the spatial direction. The proposed method is shown to be unconditionally stable and O(h4+ Δ t2) accurate. In order to check the feasibility of the proposed technique, some test examples have been considered and the simulation results are compared with those available in the existing literature. © 2019, The Author(s).
Citation Count: Amin, Muhammad...et al. (2019). "Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations", Advances in Difference Equations.
Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations
(Springer Open, 2019) Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
This paper presents a novel approach to numerical solution of a class of fourth-order time fractional partial differential equations (PDEs). The finite difference formulation has been used for temporal discretization, whereas the space discretization is achieved by means of non-polynomial quintic spline method. The proposed algorithm is proved to be stable and convergent. In order to corroborate this work, some test problems have been considered, and the computational outcomes are compared with those found in the exiting literature. It is revealed that the presented scheme is more accurate as compared to current variants on the topic.
Citation Count: Amin, Muhammad...et al. (2020). "Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions", Frontiers in Physics, Vol. 8.
Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions
(2020) Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; 56389
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 α ∈ (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 is O(h2 + Δt2−α) 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.
Citation Count: Amin, Muhammad...et al. (2021). "Redefined extended cubic B-spline functions for numerical solution of time-fractional telegraph equation", CMES - Computer Modeling in Engineering and Sciences, Vol. 127, No. 1, pp. 361-384.
Redefined extended cubic B-spline functions for numerical solution of time-fractional telegraph equation
(2021) Amin, Muhammad; Abbas, Muhammad; Baleanu, Dumitru; Iqbal, Muhammad Kashif; Riaz, Muhammad Bilal; 56389
This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.