The Adomian Decomposition Method and the Differential Transform Method for Numerical Solution of Multi-Pantograph Delay Differential Equations

Abstract

In this paper, the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM) are applied to solve the multi-pantograph delay equations. The sufficient conditions are given to assure the convergence of these methods. Several examples are presented to demonstrate the efficiency and reliability of the ADM and the DTM; numerical results are discussed, compared with exact solution. The results of the ADM and the DTM show its better performance than others. These methods give the desired accurate results only in a few terms and in a series form of the solution. The approach is simple and effective. These methods are used to solve many linear and nonlinear problems and reduce the size of computational work.

Numerical Solution of Nonlinear the Foam Drainage Equation via Hybrid Method

“…In Table 1 and Table 2, certain significant properties that would be used in the present study are presented [14,15].…”

“…In nature, chemical, physical and biological events, as well as foams are often modeled with nonlinear equations. In the literature, several methods were described and implemented for the numerical solution of these models [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. We, therefore, preferred a robust hybrid method to solve the following nonlinear foam drainage equation [1]:…”

The Comparison Study of Hybrid Method with RDTM for Solving Rosenau-Hyman Equation

“…For instance, the hybrid method has been used in the solution of several linear and nonlinear problems [25][26][27][28][29][30][31]. RDTM is used by various researchers in [13][14][15][16][17][18][19][20][21][22][23][24]. These important methods may also be potential approximate methods for in some partial differential equations [32][33][34][35][36].…”

Solution of a system of delay differential equations of multi pantograph type

“…The method based on Chebyshev polynomials, shifted Legendre approximation method, ortho exponential polynomial approach, perturbation-iteration algorithms and the Adomian decomposition method for pantograph type delay differential equations (cf. [8][9][10][11][12]).…”