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 Numerical Solution of Space-time Fractional two-dimensional Telegraph Equation by Shifted Legendre Operational Matrices

2018 ◽  
Vol 4 (1) ◽  
pp. 45-62
Author(s):  
محسن علی پور ◽  
سیده ساجده حسینی پاشاکلایی ◽  
◽  
Keyword(s):  
Numerical Solution ◽  
Telegraph Equation ◽  
Space Time ◽  
Operational Matrices ◽  
Two Dimensional

Solving systems of fractional two-dimensional nonlinear partial Volterra integral equations by using Haar wavelets

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amir Ahmad Khajehnasiri ◽  
R. Ezzati ◽  
M. Afshar Kermani
Keyword(s):  
Nonlinear System ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Fractional Integration ◽  
Volterra Integral Equations ◽  
Haar Wavelets ◽  
Operational Matrices ◽  
Two Dimensional ◽  
Numerical Examples

Abstract The main aim of this paper is to use the operational matrices of fractional integration of Haar wavelets to find the numerical solution for a nonlinear system of two-dimensional fractional partial Volterra integral equations. To do this, first we present the operational matrices of fractional integration of Haar wavelets. Then we apply these matrices to solve systems of two-dimensional fractional partial Volterra integral equations (2DFPVIE). Also, we present the error analysis and convergence as well. At the end, some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.

Numerical solution of two-dimensional first kind Fredholm integral equations by using linear Legendre wavelet

2016 ◽  
Vol 14 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Tahami ◽  
A. Askari Hemmat ◽  
S. A. Yousefi
Keyword(s):  
Integral Equation ◽  
Tensor Product ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
One Dimensional

In one-dimensional problems, the Legendre wavelets are good candidates for approximation. In this paper, we present a numerical method for solving two-dimensional first kind Fredholm integral equation. The method is based upon two-dimensional linear Legendre wavelet basis approximation. By applying tensor product of one-dimensional linear Legendre wavelet we construct a two-dimensional wavelet. Finally, we give some numerical examples.

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 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 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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