Solving The Hyperbolic Telegraph Equation Using a Modified Adomian Decomposition Method with an Invertible Partial Differential Operator

In this paper, a modified Adomian decomposition method (MADM) for solving the hyperbolic telegraph equation is proposed. The MADM introduces a new inverse partial differential operator that can speed up the convergence rate of the standard ADM. We also present a technique for converting the equation to a special case form, which makes the MADM easier to implement. The proposed method was tested on six different linear and nonlinear telegraph equations in one and two dimensions. The results show that the method is accurate and efficient for solving the telegraph equation.