In this paper, we will apply the Adomian decomposition method (ADM) to three different examples of the Telegraph Equation with a nonlinear term by the two polynomials called Adomian polynomials and the new accelerated Adomian polynomials proposed by El-kalla  that called El-kalla polynomials and compare the solution with the exact solution, we found that the new accelerated polynomials is easier and converges rapidly than Adomaian polynomials, also we found that the error between the exact solution and the solution using the new accelerated polynomials is less than the error between the exact solution and the solution using Adomian polynomials.
Y. Sayed, Ahmed.; M. Abdelgaber, K.; R. Elmahdy, A.; and L. El-Kalla, I.
"Solution of the Telegraph Equation Using Adomian Decomposition Method with Accelerated Formula of Adomian Polynomials,"
Information Sciences Letters: Vol. 10
, Article 6.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol10/iss1/6