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.
