Solution Of Telegraph Equation Research Articles

Solution of telegraph equation by double general integral transform

This paper presents a method for solving the Telegraph equation using the double general integral transform. The method involves transforming the equation into a second-order ordinary differential equation with variable coefficients, which is then solved using standard techniques. The results demonstrate the effectiveness of the method in solving the Telegraph equation.

Solution of telegraph equation by double Sumudu-Kamal transform

Solution of telegraph equation by double Sumudu-Kamal transform

Solution of Telegraph Equation by Elzaki-Laplace Transform

In this paper we have studied the combination of Elzaki and Laplace transforms to produce a degenerative new double integral transform, this new transform called the Elzaki-Laplace transform (ELT), and then applied it to some partial differential equations to find its exact solution.

New solutions of hyperbolic telegraph equation

<p style='text-indent:20px;'>We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.

The Analytical Solution of Telegraph Equation of Space-Fractional Order Derivative by the Aboodh Transform Method

In this article, an analytical solution based on the series expansion method is proposed to solve the telegraph equation of space - fractional order (TESFO), namely the Aboodh transformation method (ATM) subjected to the appropriate initial condition. Using ATM, it is possible to find exact solution or a closed approximate solution of a differential equation. Finally, several numerical examples are given to illustrate the accuracy and stability of this method.

Positive doubly periodic solutions of telegraph equations with delays

This paper deals with the existence of positive doubly periodic solutions for the nonlinear telegraph equation with delays $\mathcal{L}u=f( t, x, u(t-\tau_{1}, x),\ldots,u(t-\tau_{n}, x) )$ , $(t, x)\in\mathbb{R}^{2}$ , where $\mathcal{L}u:=u_{tt}-u_{xx}+c u_{t}+a(t, x) u $ is a linear telegraph operator acting on function $u: \mathbb{R}^{2}\to \mathbb{R}$ , $c>0$ is a constant, $a\in C(\mathbb{R}^{2}, (0, \infty))$ is 2π-periodic in t and x, $f\in C(\mathbb{R}^{2}\times[0, \infty)^{n}, [0, \infty))$ is 2π-periodic in t and x, and $\tau_{1}, \ldots, \tau_{n}\in[0, \infty)$ are constants. Some existence results of positive doubly 2π-periodic weak solutions are obtained under that $f(t, x, \eta_{1}, \ldots, \eta_{n})$ satisfies some superlinear or sublinear growth conditions on $\eta_{1}, \ldots, \eta_{n}$ . The discussion is based on the fixed point index theory in cones.

Application of polynomial scaling functions for numerical solution of telegraph equation

In this paper, we present a numerical method based on the polynomial scaling functions to solve the second-order one-space-dimensional hyperbolic telegraph equation. The method consists of expanding the approximate solution as the elements of polynomial scaling functions. The operational matrix of derivative for polynomial scaling functions is developed. Using the operational matrix of derivative, the problem reduces to a set of algebraic linear equations. An estimation of error bound for this method is investigated. Two numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces considerable accurate results among the existing scaling functions.

Homotopy Padé method for solving second-order one-dimensional telegraph equation

Purpose – The purpose of this paper is to obtain analytic solutions of telegraph equation by the homotopy Padé method. Design/methodology/approach – The authors used Maple Package to calculate the solutions obtained from the homotopy Padé method. Findings – The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m, m] homotopy Padé technique are often independent of auxiliary parameter h and this technique accelerates the convergence of the related series. Finally, numerical results for some test problems with known solutions are presented and the numerical results are given to show the efficiency of the proposed techniques. Originality/value – The paper is shown that homotopy Padé technique is a promising tool with accelerated convergence for complicated nonlinear differential equations.