Modified Reduced Differential Transform Method for Partial Differential-Algebraic Equations

Abstract

This work presents the application of the reduced differential transform method (RDTM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-two and index-three are solved to show that RDTM can provide analytical solutions for PDAEs in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful technique to find exact solutions. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend on a perturbation parameter.

On the solution of time-fractional coupled system of partial differential equations

“…In order to demonstrate the elementary idea of RDTM, let us take the nonlinear PDE of the form as follows with initial condition (IC) [35,38,39] Original function Transformed form…”

A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

“…This method is similar to the differential transform method which was first introduced by Zhou [9]. RDTM has been successfully used to many nonlinear problems [10][11][12][13][14][15][16][17][18][19] since it does not require any parameter, discretization, linearization, or small perturbations; thus it reduces the size of computational work and is easily applicable.…”

Analytical Solutions of One-Dimensional Convection-Diffusion Problems

“…Where ( ) is called t -dimensional spectrum function of ( , ). The basic definitions and fundamental operations of the two-dimensional reduced differential transform method are introduced are defined in [13] as follows: Definition 2.1. Assume ( , ) is an analytic function in the domain of interest.…”