scholarly journals Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation

2021 ◽  
Vol 127 (1) ◽  
pp. 361-384
Author(s):  
Muhammad Amin ◽  
Muhammad Abbas ◽  
Dumitru Baleanu ◽  
Muhammad Kashif Iqbal ◽  
Muhammad Bilal Riaz
Keyword(s):  
Numerical Solution ◽  
Telegraph Equation ◽  
Spline Functions ◽  
B Spline ◽  
Fractional Telegraph Equation

scholarly journals Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1154 ◽  
Author(s):  
Tayyaba Akram ◽  
Muhammad Abbas ◽  
Azhar Iqbal ◽  
Dumitru Baleanu ◽  
Jihad H. Asad
Keyword(s):  
Linear Time ◽  
Numerical Study ◽  
Numerical Approach ◽  
Telegraph Equation ◽  
High Order Accuracy ◽  
Spline Functions ◽  
B Spline ◽  
Fractional Telegraph Equation ◽  
Non Linear ◽  
Taylor’S Series

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.

scholarly journals Collocation solutions for the time fractional telegraph equation using cubic B-spline finite elements

2019 ◽  
Vol 57 (2) ◽  
pp. 131-144
Author(s):  
Orkun Tasbozan ◽  
Alaattin Esen
Keyword(s):  
Finite Elements ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Telegraph Equation ◽  
Numerical Results ◽  
Fractional Partial Differential Equations ◽  
Spline Collocation ◽  
B Spline ◽  
Fractional Telegraph Equation

Abstract In this study, we investigate numerical solutions of the fractional telegraph equation with the aid of cubic B-spline collocation method. The fractional derivatives have been considered in the Caputo forms. The L1and L2 formulae are used to discretize the Caputo fractional derivative with respect to time. Some examples have been given for determining the accuracy of the regarded method. Obtained numerical results are compared with exact solutions arising in the literature and the error norms L 2 and L ∞ have been computed. In addition, graphical representations of numerical results are given. The obtained results show that the considered method is effective and applicable for obtaining the numerical results of nonlinear fractional partial differential equations (FPDEs).

Two-Dimensional Legendre Wavelets for Solving Time-Fractional Telegraph Equation

2014 ◽  
Vol 6 (2) ◽  
pp. 247-260 ◽  
Author(s):  
M. H. Heydari ◽  
M. R. Hooshmandasl ◽  
F. Mohammadi
Keyword(s):  
Numerical Solution ◽  
Fractional Integration ◽  
Telegraph Equation ◽  
Operational Matrices ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Fractional Telegraph Equation ◽  
Manageable Method

AbstractIn this paper, we develop an accurate and efficient Legendre wavelets method for numerical solution of the well known time-fractional telegraph equation. In the proposed method we have employed both of the operational matrices of fractional integration and differentiation to get numerical solution of the time-telegraph equation. The power of this manageable method is confirmed. Moreover the use of Legendre wavelet is found to be accurate, simple and fast.

scholarly journals Extended cubic B-splines in the numerical solution of time fractional telegraph equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tayyaba Akram ◽  
Muhammad Abbas ◽  
Ahmad Izani Ismail ◽  
Norhashidah Hj. M. Ali ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Solution ◽  
Telegraph Equation ◽  
B Splines ◽  
Fractional Telegraph Equation

scholarly journals Numerical Solution of Obstacle Problems by B-Spline Functions

2011 ◽  
Vol 01 (02) ◽  
pp. 55-62
Author(s):  
G.B Loghmani ◽  
F Mahdifar ◽  
S.R Alavizadeh
Keyword(s):  
Numerical Solution ◽  
Obstacle Problems ◽  
Spline Functions ◽  
B Spline

scholarly journals A modified reproducing kernel method for a time-fractional telegraph equation

2017 ◽  
Vol 21 (4) ◽  
pp. 1575-1580 ◽  
Author(s):  
Yulan Wang ◽  
Mingjing Du ◽  
Chaolu Temuer
Keyword(s):  
Numerical Solution ◽  
Present Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Telegraph Equation ◽  
Reproducing Kernel Method ◽  
Numerical Examples ◽  
Fractional Telegraph Equation

The aim of this work is to obtain a numerical solution of a time-fractional telegraph equation by a modified reproducing kernel method. Two numerical examples are given to show that the present method overcomes the drawback of the traditional reproducing kernel method and it is an easy and effective method.

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