Elzaki Adomian decomposition method applied to Logistic differential model

Abstract

This study applies Elzaki Adomian Decomposition Method (EADM) to solve the Logistic Differential Model (LDM) of different forms and coefficients. Illustrative examples are considered, and the obtained results are in good agreement compared to those already in the literature. This study, therefore, recommends the proposed method (EADM) for application in other aspects of applied mathematics for real-life problems.

Coupling the SBA Method and the Elzaki Transformation to Solve Nonlinear Fractional Differential Equations

“…Commonly used numerical methods are the variational iteration method (VIM) [1,2], the Adomian decompositional method (ADM) [3,4,5], and the generalized differential transformation method (GDTM) [6,7] .Recently, the SBA method [8,9,10] which is a combination of the Adomian method, the method of successive approximations [11,12] and the Picard principle, is also used. The nonlinear fractional differential equations are also solved with techniques combining numerical methods with integral transformations, such as the Homotopy perturbation method combined with the Elzaki transformation (EHTPM) [13,14], the Homotopy perturbation method combined with the Sumudu transformation (HPSTM) [15], the Adomian decomposition method combined with the Elzaki transformation (EADM) [16]. The discretization methods are also used [17,18].…”