New numerical study of Adomian method applied to a diffusion model

Abstract

We prove in this paper the convergence of Adomian method applied to linear or nonlinear diffusion equations. The results show that the convergence of this method is not influenced by the choice of the linear inversible operator L in the equation to be solved. Furthermore we give some particular examples about a new canonical form where the initial value u 0 of Adomian series is chosen in some special form which verifies the initial and boundary conditions. Then Adomian series converges to exact solution or all approximated (truncated series) solutions verify these conditions.

Solving Burger's equation by semi-analytical and implicit method

“…Here, we will study the convergence analysis as same manner in [37] of the LADM applied to the Burgers' equation. Let us consider the Hilbert space H which may define by H = L 2 ((α, β)X[0, T]) the set of applications:…”

“…The LADM is convergence if the following two hypotheses are satisfied: [37] and the references therein). Theorem 1.…”

Application of the Adomian decomposition method and Laplace transform method to solving the convection diffusion-dissipation equation

“…The general theory of the Adomian decomposition method can be found in [1][2][3][4][5][6][7][8][9][10].…”

Application of the Fourier transform via Adomian's decomposition method

“…Sadigh Behzadi, solving nonlinear volterra fredholm integro-differential equations using the modified Adomian decomposition method [10]. Also, there exist some recently published papers with some modifications about application of the Adomain decomposition method to solve a differential equation [5,16,17,18]. Adomain gives the solution as an infinite series usually converging to an accurate solution.…”