Solutions of One-Dimensional Second-Order Nonlinear Hyperbolic Telegraph Equation via Multistep Modified Reduced Differential Transform Method.

Abstract

The main purpose of this study was to find approximate analytical solutions of a one dimensional second-order nonlinear hyperbolic telegraph equation subject to the given initial conditions by the multistep modified reduced differential transform method (MMRDTM). The main advantage of this method is that it can be applied directly to nonlinear differential equations without linearization, discretion, or perturbation and it reduces significantly the computational work. Some properties and theorems which are useful for this study are proved. Numerical examples are carried out to check the accuracy, efficiency, and convergence of the described method. The solution is obtained in the form of an infinite series with easily computable components. Graphical results are shown to represent the behavior of the solutions to demonstrate the validity and accuracy of the MMRDTM. The study result shows that the analytical approximate solutions converge very rapidly to the exact solutions, and further the proposed technique is simply applicable and accurate.