WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

Browse

Filters

2015 - 20203

Settings

Publisher: search.filters.publisher.SpringerSubject: search.filters.subject.Collocation Method

Search Results

Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    An Iterative Algorithm for Robust Simulation of the Sylvester Matrix Differential Equations
    (Springer, 2020) Beik, Samaneh Panjeh Ali; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem
    This paper proposes a new effective pseudo-spectral approximation to solve the Sylvester and Lyapunov matrix differential equations. The properties of the Chebyshev basis operational matrix of derivative are applied to convert the main equation to the matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained equations. Also, the error analysis of the propounded method is presented, which reveals the spectral rate of convergence. To illustrate the effectiveness of the proposed framework, several numerical examples are given.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 37
    Extended 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, Tayyaba
    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.
  • Article
    Citation - WoS: 31
    Citation - Scopus: 35
    A Jacobi Gauss-Lobatto and Gauss-Radau Collocation Algorithm for Solving Fractional Fokker-Planck Equations
    (Springer, 2015) Ezz-Eldien, Samer S.; Bhrawy, Ali H.; Ahmed, Engy A.; Baleanu, Dumitru; Hafez, Ramy M.
    In this article, we construct a new numerical approach for solving the time-fractional Fokker-Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss-Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss-Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker-Planck equation and the time-space-fractional Fokker-Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm.