Adomian method for solving Emden-Fowler equation of higher order

Dabwan, Nuha Mohammed; Hasan, Yahya Qaid

doi:10.37418/amsj.9.1.19

Cited by 2 publications

(1 citation statement)

References 7 publications

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“…Many analytical and numerical methods have been established. Different powerful mathematical techniques such as Adomian Decomposition Method (ADM) [1][2][3], Sumudu transform [4], Sumudu Adomian Decomposition method (SADM) [5][6][7], homotopy perturbation method (HPM), Laplace decomposition method (LDM) [8], Padé approximant [9][10][11][12][13], Laplace transform combined with Padé approximation [14], homotopy perturbation Sumudu transform method (HPSTM) [15], Homotopy Padé Approximate [16], Modified Adomian Decomposition Method [17][18][19], Homotopy Laplace transform [20], Akbari-Ganji's Method (AGM) [21][22][23], and Hopf bifurcation [24] have been proposed to obtain exact and approximate analytic solutions.…”

Section: Introductionmentioning

confidence: 99%

Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation

Richard

Zhang

2021

Journal of Applied Mathematics

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The main purpose of this paper is to solve the nonlinear Schrödinger equation using some suitable analytical and numerical methods such as Sumudu transform, Adomian Decomposition Method (ADM), and Padé approximation technique. In many literatures, we can see the Sumudu Adomian decomposition method (SADM) and the Laplace Adomian decomposition method (LADM); the SADM and LADM provide similar results. The SADM and LADM methods have been applied to solve nonlinear PDE, but the solution has small convergence radius for some PDE. We perform the SADM solution by using the function P L / M · called double Padé approximation. We will provide the graphical numerical simulations in 3D surface solutions of each application and the absolute error to illustrate the efficiency of the method. In our methods, the nonlinear terms are computed using Adomian polynomials, and the Padé approximation will be used to control the convergence of the series solutions. The suggested technique is successfully applied to nonlinear Schrödinger equations and proved to be highly accurate compared to the Sumudu Adomian decomposition method.

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