The Adomian decomposition method in turning point problems

A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method

“…Over the last 25 years, the Adomian decomposition method (ADM) and its modification (MADM) [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] have been used to solve effectively and easily a large class of linear and nonlinear ordinary and partial differential equations. However, little attention was devoted to their applications in solving the singular two-point boundary value problems.…”

Solving Systems of Non-Linear Volterra Integral Equations by Combined Sumudu Transform-Adomian Decomposition Method

“…In the beginning of the 1980's, Adomian [5,6] proposed a new and fruitful method, so-called the Adomian decomposition method (ADM), for solving linear and non-linear (algebraic, differential, partial differential, integral, etc.) equations [7][8][9][10][11][12][13][15][16][17]. It has been shown that this method yields a rapid convergence of the solutions series.…”

“…These methods solve high order FIVPs directly without reducing them into first order system [14][15][16][17][18][19]. The accuracy of the approximate solution can also be determined without needing the exact solution, especially in the nonlinear equations [7,9,11]. In recent years, many new methods, such as He's homotopy perturbation method [13,20,21], modified homotopy perturbation method [22], Adomian decomposition method [13,23], variational iteration methods [13,24,25], and many more, were used to solve integral and integro-differential equations.…”

Novel insights into the computational techniques in unsteady MHD second‐grade fluid dynamics with oscillatory boundary conditions

“…The main advantage of ADM is that it can be applied directly for all types of differential and integral equations. A comprehensive discussion has been provided in the studies of Adomian, 65 Wazwaz, 66 Babolian and Davari, 67 and Al‐Hayani and Casasus 68 . A relevant work can also be seen in the studies of Mehta et al 69 and Mabood et al 70…”