Abstract
Abstract In this study, a robust hybrid method is used as an alternative method, which is a different method from other methods for the approximate of the telegraph equation. The hybrid method is a mixture of the finite difference and differential transformation methods. Three numerical examples are solved to prove the accuracy and efficiency of the hybrid method. The reached results from these samples are shown in tables and graphs.
Highlights
IntroductionThe preferred hybrid method is used for solving many types of differential equations
In this study, a robust hybrid method is used as an alternative method, which is a different method from other methods for the approximate of the telegraph equation
Several numerical methods were developed for solving 1D telegraph equation, for example, reduced differential transform method, differential quadrature method, new unconditionally stable difference schemes, Chebyshev tau method, dual reciprocity boundary integral equation, cubic B-spline collocation method, modified B-spline differential quadrature method, semi-discretization method, unconditionally stable ADI method, Rothe-wavelet method, collocation method, He’s variational iteration method, dual reciprocity boundary integral equation method, etc. [1, 9,10,11,12,13,14,15,16,17,18,19]
Summary
The preferred hybrid method is used for solving many types of differential equations. The other differential equation types can be solved by this hybrid method [25,26,27,28,29,30,31,32]. The hybrid method is given as a blend of the differential transform and the finite difference methods. The differential transform method was proposed by Zhou for the solution of linear and nonlinear differential equations for electrical circuit analysis [24]. This method was developed by Chen and Ho for partial differential equations [5]. The approximate solution of the telegraph equation as different from the other methods is obtained from a very powerful iterative scheme
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