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The modeling of many phenomena in various fields such as mathematics,physics, chemistry, engineering, biology, and astronomy is done by thenonlinear partial differential equations (PDE). The hyperbolic telegraphequation is one of them, where it describes the vibrations of structures (e.g.,buildings, beams, and machines) and are the basis for fundamental equations ofatomic physics. There are several analytical and numerical methods are used tosolve the telegraph equation. An analytical solution considers framing theproblem in a well-understood form and calculating the exact resolution. It alsohelps to understand the answers to the problem in terms of accuracy andconvergence. These analytic methods have limitations with accuracy andconvergence. Therefore, a novel analytic approximate method is proposed to dealwith constraints in this paper. This method uses the Taylors' series in itsderivation. The proposed method has used for solving the second-order,hyperbolic equation (Telegraph equation) with the initial condition. Threeexamples have presented to check the effectiveness, accuracy, and convergenceof the method. The solutions of the proposed method also compared with thoseobtained by the Adomian decomposition method (ADM), and the Homotopy analysismethod (HAM). The technique is easy to implement and produces accurate results.In particular, these results display that the proposed method is efficient andbetter than the other methods in terms of accuracy and convergence.

A novel analytic method for solving linear and nonlinear Telegraph Equation