Numerical treatment on one-dimensional hyperbolic telegraph equation by the method of line-group preserving scheme

2019 ◽  
Vol 134 (4) ◽  
Author(s):  
M. S. Hashemi ◽  
M. Inc ◽  
E. Karatas ◽  
E. Darvishi
Keyword(s):  
Telegraph Equation ◽  
Numerical Treatment ◽  
One Dimensional ◽  
Group Preserving Scheme

scholarly journals On a Generalization of One-Dimensional Kinetics

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1264
Author(s):  
Vladimir V. Uchaikin ◽  
Renat T. Sibatov ◽  
Dmitry N. Bezbatko
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Constant Velocity ◽  
Telegraph Equation ◽  
Material Derivative ◽  
Symmetric Random Walk ◽  
One Dimensional ◽  
Special Cases ◽  
Fractional Telegraph Equation ◽  
Asymmetric Case

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.

scholarly journals SYMMETRY ANALYSIS OF TELEGRAPH EQUATION

2011 ◽  
Vol 04 (01) ◽  
pp. 117-126
Author(s):  
Mehdi Nadjafikhah ◽  
Seyed-Reza Hejazi
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Telegraph Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Group Method ◽  
Parameter Group ◽  
One Dimensional

Lie symmetry group method is applied to study the telegraph equation. The symmetry group and one-parameter group associated to the symmetries with the structure of the Lie algebra symmetries are determined. The reduced version of equation and its one-dimensional optimal system are given.

A Galerkin-Type Method to Solve One-Dimensional Telegraph Equation Using Collocation Points in Initial and Boundary Conditions

2018 ◽  
Vol 15 (05) ◽  
pp. 1850031 ◽  
Author(s):  
Şuayip Yüzbaşı ◽  
Murat Karaçayır
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Telegraph Equation ◽  
Inner Product ◽  
Present Scheme ◽  
One Dimensional ◽  
Collocation Points ◽  
Correction Technique ◽  
Initial And Boundary Conditions ◽  
Residual Correction

In this study, a Galerkin-type approach is presented in order to numerically solve one-dimensional hyperbolic telegraph equation. The method includes taking inner product of a set of bivariate monomials with a vector obtained from the equation in question. The initial and boundary conditions are also taken into account by a suitable utilization of collocation points. The resulting linear system is then solved, yielding a bivariate polynomial as the approximate solution. Additionally, the technique of residual correction, which aims to increase the accuracy of the approximate solution, is discussed briefly. The method and the residual correction technique are illustrated with four examples. Lastly, the results obtained from the present scheme are compared with other methods present in the literature.

scholarly journals A Collocation Method for Numerical Solution of Hyperbolic Telegraph Equation with Neumann Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
R. C. Mittal ◽  
Rachna Bhatia
Keyword(s):  
Boundary Conditions ◽  
Numerical Experiments ◽  
Neumann Boundary ◽  
Telegraph Equation ◽  
Neumann Boundary Conditions ◽  
Basis Functions ◽  
One Dimensional ◽  
First Order ◽  
Spline Basis ◽  
Good Agreement

We present a technique based on collocation of cubic B-spline basis functions to solve second order one-dimensional hyperbolic telegraph equation with Neumann boundary conditions. The use of cubic B-spline basis functions for spatial variable and its derivatives reduces the problem into system of first order ordinary differential equations. The resulting system subsequently has been solved by SSP-RK54 scheme. The accuracy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and in good agreement with the exact solution.

scholarly journals The Telegraph Equation and Its Solution by Reduced Differential Transform Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vineet K. Srivastava ◽  
Mukesh K. Awasthi ◽  
R. K. Chaurasia ◽  
M. Tamsir
Keyword(s):  
Telegraph Equation ◽  
Differential Transform Method ◽  
Mathematical Technique ◽  
Science And Engineering ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Wide Range ◽  
Differential Transform ◽  
Reduced Differential Transform Method

One-dimensional second-order hyperbolic telegraph equation was formulated using Ohm’s law and solved by a recent and reliable semianalytic method, namely, the reduced differential transform method (RDTM). Using this method, it is possible to find the exact solution or a closed approximate solution of a differential equation. Three numerical examples have been carried out in order to check the effectiveness, the accuracy, and convergence of the method. The RDTM is a powerful mathematical technique for solving wide range of problems arising in science and engineering fields.

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