scholarly journals Numerical solution of time-fractional telegraph equation by using a new class of orthogonal polynomials

2022 ◽  
Vol 40 ◽  
pp. 1-13
Author(s):  
Fakhrodin Mohammadi ◽  
Hossein Hassani
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Numerical Solution ◽  
Collocation Method ◽  
Operational Matrix ◽  
Telegraph Equation ◽  
New Class ◽  
Fractional Telegraph Equation ◽  
Collocation Approach ◽  
Chelyshkov Polynomials

‎In this article‎, ‎an efficient numerical method based on a new class of orthogonal polynomials‎, ‎namely Chelyshkov polynomials‎, ‎has been presented to approximate solution of time-fractional telegraph (TFT) equations‎. ‎The fractional operational matrix of the Chelyshkov polynomials along with the typical collocation method is used to reduces TFT equations to a system of algebraic equations‎. ‎The error analysis of the proposed collocation method is also investigated‎. ‎A comparison with other published results confirms that the presented Chelyshkov collocation approach is efficient and accurate for solving TFT equations‎. ‎Illustrative examples are included to demonstrate the efficiency of the Chelyshkov method‎.

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 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 Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion equation by using collocation method

2021 ◽  
Vol 29 (2) ◽  
pp. 211-230
Author(s):  
Manpal Singh ◽  
S. Das ◽  
Rajeev ◽  
E-M. Craciun
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Operational Matrix ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Existing Problems ◽  
Advection Diffusion Equation ◽  
Error Analyses ◽  
Nonlinear Algebraic Equations ◽  
Accurate Numerical Solution

Abstract In this article, two-dimensional nonlinear and multi-term time fractional diffusion equations are solved numerically by collocation method, which is used with the help of Lucas operational matrix. In the proposed method solutions of the problems are expressed in terms of Lucas polynomial as basis function. To determine the unknowns, the residual, initial and boundary conditions are collocated at the chosen points, which produce a system of nonlinear algebraic equations those have been solved numerically. The concerned method provides the highly accurate numerical solution. The accuracy of the approximate solution of the problem can be increased by expanding the terms of the polynomial. The accuracy and efficiency of the concerned method have been authenticated through the error analyses with some existing problems whose solutions are already known.

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

The meshless method of radial basis functions for the numerical solution of time fractional telegraph equation

2014 ◽  
Vol 24 (8) ◽  
pp. 1636-1659 ◽  
Author(s):  
Akbar Mohebbi ◽  
Mostafa Abbaszadeh ◽  
Mehdi Dehghan
Keyword(s):  
Radial Basis Functions ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Telegraph Equation ◽  
Basis Functions ◽  
Content Type ◽  
Fractional Telegraph Equation ◽  
Radial Basis ◽  
Collocation Approach ◽  
Derivatives Of

Purpose – The purpose of this paper is to show that the meshless method based on radial basis functions (RBFs) collocation method is powerful, suitable and simple for solving one and two dimensional time fractional telegraph equation. Design/methodology/approach – In this method the authors first approximate the time fractional derivatives of mentioned equation by two schemes of orders O(τ3−α) and O(τ2−α), 1/2<α<1, then the authors will use the Kansa approach to approximate the spatial derivatives. Findings – The results of numerical experiments are compared with analytical solution, revealing that the obtained numerical solutions have acceptance accuracy. Originality/value – The results show that the meshless method based on the RBFs and collocation approach is also suitable for the treatment of the time fractional telegraph equation.

Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method

2017 ◽  
Vol 18 ◽  
pp. 50-59 ◽  
Author(s):  
S.C. Shiralashetti ◽  
R.A. Mundewadi
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Collocation Method ◽  
Haar Wavelet ◽  
Fredholm Integral Equations ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Wavelet Collocation Method

In this paper, we present a numerical solution of nonlinear Volterra-Fredholm integral equations using Haar wavelet collocation method. Properties of Haar wavelet and its operational matrices are utilized to convert the integral equation into a system of algebraic equations, solving these equations using MATLAB to compute the Haar coefficients. The numerical results are compared with exact and existing method through error analysis, which shows the efficiency of the technique.

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