An approximation to the solution of telegraph equation by Adomian decomposition method

Abstract

Adomian decomposition method has been applied to solve many functional equations so far. In this article, this method is applied to solve a famous partial differential equation, called Telegraph equation.

Stability of a Numerical Method for a Space-time-fractional Telegraph Equation

“…Combining (1) and (2), we see that the voltage u(t, x) satisfies the classical telegraph equation ∂ 2 u(t, x) ∂t 2 + a ∂u(t, x) ∂t + bu(t, x) = c 2 ∂ 2 u(t, x) ∂x 2 , t > 0, x > 0,…”

Analysis of Solutions of Time Fractional Telegraph Equation

“…Homogeneous Fractional Telegraph Equation. Let us consider the time fractional telegraph equation [8,13,16,19]…”

“…Wazwaz [31] has explored this method to obtain solutions of wave equation. The classical telegraph equation and space or time fractional telegraph equations have been solved by a number of researchers namely Biazar et al [6,8,7], Cascaval et al [9], Kaya [19], Momani [22], Odibat and Momani [33], Orsingher and Zhao [25], Orsingher and Beghin [24], Sevimlican [30] and Yildirim [32] using various techniques such as variational iteration method, transform method, Adomian decomposition method, generalized differential transform method, and homotopy perturbation method. Adomian decomposition offers certain advantages over routine numerical methods.…”

“…A mathematical derivation for the time fractional telegraph equation is obtained from classical telegraph equation by replacing the second order time derivative by fractional derivative of order 1 < 2α ≤ 2 and by replacing first order time derivative by fractional derivative of order 1 2 < α ≤ 1. The modeling of time fractional telegraph equation [8] is as follows.…”

An approximation to the solution of telegraph equation by variational iteration method

“…Mathematical modeling of telegraph equation is well addressed in Ref., [1], in which the authors have solved the equation by Adomian decomposition method. The general form of equation is as follows:…”