A new Approach to Find Exact and Approximate Solutions to PDEs in Different Dimensions

Abstract

In this research article, We present an algorithm called the Reduced Differential Transform Method (RDTM) to find exact and approximate solutions to different types of linear and nonlinear partial differential equations (PDEs) in different dimensions such as, nonhomogeneous parabolic equation, the Zakharov--Kuznetsov (ZK) equation, and the fifth order nonlinear Caudrey--Dodd--Gibbon (CDG) equation. The study outlines the significance of the method and the results showed that the method reduces the numerical calculations. The examples we present in this paper reveal that the proposed method is very effective, simple and
can be applied to other nonlinear partial differential equations
models in the area of Mathematical Physics and Engineering. 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. 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).