On the solution of algebraic equations by the decomposition method

An improved algorithm for calculation of the natural gas compressibility factor via the Hall‐Yarborough equation of state

“…[22,23] It can provide exact analytical solutions to a wide class of linear or nonlinear functional equations, and systems of such equations, such as ordinary differential equations, [24,25] partial differential equations, [26,27] integral equations, [28][29][30] integro-differential equations, [31][32][33] algebraic equations, [34][35][36] differential-algebraic, [37,38] differential-difference equations, [39] etc. The mathematical literature on applications of the ADM in the study of problems arising from the applied sciences and engineering is very extensive.…”

Homotopy perturbation method for homogeneous Smoluchowsk's equation

“…(12) with initial condition given in Eq. (13) by Adomian decomposition method (ADM) [13][14][15][16], it can be written as follows:…”

Sur la convergence de la méthode d'Adomian

“…Dans de très nombreux papiers [1,2,3], Adomian propose l'utilisation d'une technique numérique basée sur l'utilisation de polynômes qui portent son nom. Cette technique a l'avantage de l'élégance et surtout de la facilité d'utilisation.…”

“…-pour la résolution numérique d'équations algébriques non linéaires [2]; -pour la résolution d'équations différentielles [6] ayant éventuellement des retards [4]; 292 Y. CHERRUAULT -pour l'approximation des solutions d'équations aux dérivées partielles [12] non linéaires.…”