An improvement to an alternate algorithm for computing Adomian polynomials in special cases

In a published article entitled “An alternate algorithm for computing Adomian polynomials, in special cases” by the first author and some of his collaborators, the algorithm were applied in special cases which restricts the application of the algorithm. In this article new ideas are suggested for applying the algorithm in any cases without any more assumptions. Some examples are presented to illustrate the applications of the algorithm in more comprehensive situations, and also to show the ability and simplicity of the algorithm.