Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations

Abstract

Reduced differential transform method to solve 5 two and three dimensional second order hyperbolic 6 telegraphic equations Q1 7 Abstract In this article, an analytical solution procedure is described for solving two and three dimensional second order hyperbolic telegraph equation Q3 using a reliable semi-analytic method so called the reduced differential transform method (RDTM) subject to the appropriate initial condition. Using this method, it is possible to find an exact solution or a closed approximate solution of a differential equation. Various numerical examples are carried out to check the accuracy, efficiency, and convergence of the described method. The method is a powerful mathematical tool for solving a wide range of problems arising in engineering and sciences.

A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations

“…It is an iterative procedure based on the use of the Taylor series solution of differential equations. It has been successfully applied to solve various nonlinear partial differential equations [13]- [27]. Since it does not require any parameter, discretization, linearization or small perturbations, thus it reduces the size of computations and can be easily used.…”

“…Since it does not require any parameter, discretization, linearization or small perturbations, thus it reduces the size of computations and can be easily used. The RDTM was used for solving the generalized Korteweg-de Vries equation [14], the fractional Benney-Lin equation [15], the Wu-Zhang equation [16], the equal width wave equation and the inviscid Burgers equation [17], the Sine-Gordon equation [18], the Burgers and Huxley equations [19], the time-fractional telegraph equation [20], the generalized Drinfeld-Sokolov equations and Kaup-Kupershmidt equation [21], the Zakharov-Kuznetsov equations [22], the heat-like equations [23], the coupled Ramani equations [25], two integral members of nonlinear Kadomtsev-Petviashvili hierarchy equations [26], and the second order hyperbolic telegraph equation [27]. Few studies have been applied RDTM to solve the Navier-Stocks equations, which is one of the reasons for choosing it as a method for solving the lid-driven cavity flow.…”

Solving three-dimensional Volterra integral equation by the reduced differential transform method

“…In this section, we present basic definitions and operations of the reduced differential transform method, for more details see [12]and the references therein. Now, assume that the function of three variables w(x, y,t) can be written as a multiple of two functions as follows: w(x, y,t) = F(x, y)G(t), then w(x, y,t) can be represented as:…”

Application of the SBA method for solving partial differential equations

“…These last years, several types of linear and nonlinear partial differential equations have been solved, using different techniques like: Homotopy Perturbation [1], Adomian decomposition method [2]- [7], The Reduced Differential Transform Method [8]- [10] , and others. Here we use the SBA method to find the exact solution of: the nonlinear homogenous and non-homogenous gas dynamic equations [11]- [16] and the two-dimensional partial differential initial boundary value problem [1] .…”