Abstract In this paper, a general framework of the reduced differential transform method is presented for solving the regularized long wave (RLW) equation. In this method, the solution is calculated in the form of convergent power series with easily computable components. The efficiency of the considered method is illustrated by some examples. The results show that the proposed iteration techni...

Corresponding Author: Mohammed Al-Smadi Department of Applied Science, Ajloun College, AlBalqa Applied University, Ajloun 26816, Jordan Email: [email protected] Abstract: This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Red...

In this paper, the reduced differential transform method is used for solving the initial value problem of the porous medium equation that usually occurs in nonlinear problems of heat and mass transfer and also in biological systems. A complete description of the method is derived. Finally, to show the efficiency of the presented method, four examples are given. MSC: 35G25 • 35A22

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is base...

Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Diff...

The differential transform method and Herrera’s complex integral method are shown to be related through the Taylor-Cauchy transform, which appears as a genuine fore-runner of both methods. A short discussion of this result is provided. Mathematics Subject Classification: 34A05, 34A25, 34A30, 34A34, 35C10

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...

Muhammad Idrees and Fazal Muhammad ABSTRACT In this paper, Differential Transform Method (DTM) is proposed for the closed form solution of linear and non-linear stiff systems. This method gives the series of solutions which can easily be converted into exact solution. The method is described and illustrated with the help of examples. The results show that DTM is very easy, effective and conveni...