Numerical Solution of Telegraph Equation Using Bernoulli Collocation Method

2018 ◽  
Vol 89 (4) ◽  
pp. 769-775
Author(s):  
Kübra Erdem Biçer ◽  
Salih Yalçinbaş
Keyword(s):  
Numerical Solution ◽  
Collocation Method ◽  
Telegraph Equation

Numerical solution for the fractional-order one-dimensional telegraph equation via wavelet technique

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kumbinarasaiah Srinivasa ◽  
Hadi Rezazadeh
Keyword(s):  
Analytical Solution ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Collocation Method ◽  
Fractional Order ◽  
Numerical Technique ◽  
Telegraph Equation ◽  
Algebraic Equations ◽  
One Dimensional ◽  
Wavelet Collocation Method

AbstractIn this article, we proposed an efficient numerical technique for the solution of fractional-order (1 + 1) dimensional telegraph equation using the Laguerre wavelet collocation method. Some examples are illustrated to inspect the efficiency of the proposed technique and convergence analysis is discussed in terms of a theorem. Here, the fractional-order telegraph equation is converted into a system of algebraic equations using the properties of the Laguerre wavelet, and solutions obtained by the proposed scheme are more accurate and they are compared with the analytical solution and other method existed in the literature.

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.

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