scholarly journals He’s polynomials method for analytical solutions of telegraph equation

Author(s):  
S O Edeki ◽  
O M Ofuyatan ◽  
G O Akinlabi
2021 ◽  
pp. 2150324
Author(s):  
Mostafa M. A. Khater ◽  
Dianchen Lu

In this paper, the stable analytical solutions’ accuracy of the nonlinear fractional nonlinear time–space telegraph (FNLTST) equation is investigated along with applying the trigonometric-quantic-B-spline (TQBS) method. This investigation depends on using the obtained analytical solutions to get the initial and boundary conditions that allow applying the numerical scheme in an easy and smooth way. Additionally, this paper aims to investigate the accuracy of the obtained analytical solutions after checking their stable property through using the properties of the Hamiltonian system. The considered model for this study is formulated by Oliver Heaviside in 1880 to define the advanced or voltage spectrum of electrified transmission, with day-to-day distances from the electrified communication or the application of electromagnetic waves. The matching between the analytical and numerical solutions is explained by some distinct sketches such as two-dimensional, scatter matrix, distribution, spline connected, bar normal, filling with two colors plots.


2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Adebayo O. Adewumi ◽  
Saheed O. Akindeinde ◽  
Adebayo A. Aderogba ◽  
Babatunde S. Ogundare

This article presents a new numerical scheme to approximate the solution of one-dimensional telegraph equations. With the use of Laplace transform technique, a new form of trial function from the original equation is obtained. The unknown coefficients in the trial functions are determined using collocation method. The efficiency of the new scheme is demonstrated with examples and the approximations are in excellent agreement with the analytical solutions. This method produced better approximations than the ones produced with the standard weighted residual methods.


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