On Finding Exact and Approximate Solutions to Some PDEs Using the Reduced Differential Transform Method

Abstract

Abstract:In this research article, we give analytic approximate solution to the Sharma Tasso Olver (STO) equation and exact solutions to both the Schrodinger equation and the Telegraph equation. Also, the approximate analytical and exact solutions we present in this paper are calculated in the form of power series with easily computable components. The obtained results are in a good agreement with the exact solutions. We present an algorithm called the Reduced Differential Transform Method (RDTM) to find approximate solution and we compare the results with the exact solutions. This method reduces significantly the numerical computations compare with the existing methods such as the perturbation technique, differential transform method (DTM) and the Adomian decomposition method (ADM).

An Approximate Solution of Fractional Kolmogorov-Petrovskii-Piskunov Equations

“…Selected basic operations and proofs can be found in [9,[21][22][23][24]. Table 1 lists the basic operations of FRDTM.…”

Approximate solutions of coupled Ramani equation by using RDTM with compared DTM and exact solutions

“…And also, unlike the DTM, RDTM is based on the Poisson series coefficients expansion. By using the literature [24], [26,27,28,29,30,31], we present the RDTM as follow.…”

Finding exact solutions of nonlinear PDEs using the natural decomposition method

“…In physics, for example, the heat flow and the wave propagation phenomena are well described by PDEs . Recently, there has been a great amount of research aiming to find methods for solutions of nonlinear PDEs, and many new approaches have been proposed, for example, the variational iteration method , the homotopy perturbation method , the Laplace transformation , and the reduced differential transform method . We present a new integral transform method called the natural decomposition method (NDM) and apply it to find exact solutions to nonlinear PDEs.…”