The Numerical Study of a Hybrid Method for Solving Telegraph Equation

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.

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

“…Solving the telegraph equation analytically is not always possible or convenient, especially when the boundary and initial conditions are complicated or nonlinear. Therefore, various numerical and approximate methods have been proposed and used to obtain solutions of the telegraph equation [3,4,5,6,7,8,9,10,11], such as finite difference methods, Runge-Kutta methods, perturbation methods, homotopy methods, and Adomian decomposition method (ADM). Among these methods, ADM is a popular and powerful technique that can handle linear and nonlinear problems without linearization or discretization.…”

Laplace Projected Differential Transform Method for Solving Nonlinear Partial Differential Equations

“…Hybrid method is the incorporated form of two or even more approaches used to solve many forms of differential equations, which include the logistics-differential equations [15], partial differential equations [3,4,7,17,24,26,31,33,35], integro-differential equation [5,6,36] and fractional differential equations [28,29,32]. A number of the hybrid method found in the literature feature: Laplace homotopy perturbation method (LHPM) [22,34], which incorporates the Laplace transform and homotopy pertubation method(HPM); RBF-based DQ method [31], which incorporates global radial basis function-based and differential quadrature method; homotopy perturbation and Sumudu transform Method [14], which incorporates the Sumudu transform and homotopy perturbation method; Laplace Adominan decomposition method (LADM) [28,32,36], which incorporates the Laplace transform and Adomian decomposition method (ADM); Laplace differential transform method (LDTM) [8,9], which incorporates Laplace transform and differential transform method (DTM); Laplace Decomposition method [15,17]; Finite difference and differential transform method [7]; Homotopy perturbation and Elzaki transform [12]. However, many of these hybrid approaches entails perturbation, linearization or any other transformation and at the same time entails a ton of computational efforts.…”

Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method

“…Jonathan Lenells provided foundation for the geometric study of HS equation, this exhibits a geodesic flow. The system of nonlinear DEs like Hunter-Saxton, Camassa-Holm and Degasperis-Procesi was analyzed by variational principle to find the weak solutions in [8] , Volterra-Fredholm integral equations [9] , Boussinesq equations [10] , Schrödinger equation [11] , [12] , telegraph PDEs [13] , [14] , Burgers equation [15] . There are several researches in the literature, that are examined by the different techniques [16] , [17] , [18] , [19] , [20] .…”