Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
6 results
Search Results
Article Citation - WoS: 2Citation - Scopus: 3An Inverse Problem of Reconstructing the Time-Dependent Coefficient in a One-Dimensional Hyperbolic Equation(Springer, 2021) Abbas, Muhammad; Baleanu, Dumitru; Huntul, M. J.In this paper, for the first time the inverse problem of reconstructing the time-dependent potential (TDP) and displacement distribution in the hyperbolic problem with periodic boundary conditions (BCs) and nonlocal initial supplemented by over-determination measurement is numerically investigated. Though the inverse problem under consideration is ill-posed by being unstable to noise in the input data, it has a unique solution. The Crank-Nicolson-finite difference method (CN-FDM) along with the Tikhonov regularization (TR) is applied for calculating an accurate and stable numerical solution. The programming language MATLAB built-in lsqnonlin is used to solve the obtained nonlinear minimization problem. The simulated noisy input data can be inverted by both analytical and numerically simulated. The obtained results show that they are accurate and stable. The stability analysis is performed by using Fourier series.Article Citation - WoS: 52Citation - Scopus: 57A 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, NaumanWe 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: 18Citation - Scopus: 22A Fourth Order Non-Polynomial Quintic Spline Collocation Technique for Solving Time Fractional Superdiffusion Equations(Springer, 2019) Abbas, Muhammad; Iqbal, Muhammad Kashif; Ismail, Ahmad Izani Md.; Baleanu, Dumitru; Amin, MuhammadThe 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(h(4) + Delta t(2)) 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.Article Citation - WoS: 27Citation - Scopus: 31Non-Polynomial Quintic Spline for Numerical Solution of Fourth-Order Time Fractional Partial Differential Equations(Springer, 2019) Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Amin, MuhammadThis 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.Article Citation - WoS: 33Citation - Scopus: 37Extended Cubic B-Splines in the Numerical Solution of Time Fractional Telegraph Equation(Springer, 2019) Abbas, Muhammad; Ismail, Ahmad Izani; Ali, Norhashidah Hj M.; Baleanu, Dumitru; Akram, TayyabaA 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.Article Citation - WoS: 23Citation - Scopus: 28A 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, NaumanIn 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.