Convergence of Adomian’s method applied to algebraic equations

Abstract

Considers the convergence of Adomian's method applied to algebraic equations. Presents directly some conditions of convergence which only depend on the equations' coefficients and also gives an estimation of the truncation error together with some numerical applications.

An iterative method for solving nonlinear functional equations

“…x ≈ x 0 + · · · + x 5 = −0.06157535114, which matches with the approximate solution given by Ouedraogo et al [11]. Their answer is x = −0.06157535132499062.…”

Solving a class of linear partial differential equations with Dirichlet‐boundary conditions by the Adomian method

“…For a good understanding of this work we briefly recall some results about Adomian method (Abbaoui, 1995;Abbaoui et al, , 2001Himoun et al, 1999;Ngarhasta et al, 2002;Ouerdraogo et al, 2000).…”

Approximate analytical solution of fourth order boundary value problems

“…In [12] we investigate the convergence of the method as applied to second order BVPs. Relevant results on convergence of this method can be found in [4,5,11,15,18,22]. In a paper of Wazwaz [28] some numerical results are given for several higher order problems where the exact solutions are known.…”