A new decomposition method based on infinite products

Abstract

PurposeThe purpose is to apply a new decomposition method for solving non‐linear functional equations.Design/methodology/approachThe method used is similar to the Adomian decomposition method (ADM). In this approach, Adomian's original solution for solving non‐linear functional equations and Cherruault's proposed new definition of ADM are replaced by a new decomposition technique.FindingsAdomian gives the solution using his decomposition method as an infinite series usually converging to an accurate solution. Cherruault's new definition also proved the convergence under suitable conditions and a reasonable hypothesis. This paper has developed a new decomposition technique based on infinite products. It was found that it then became possible to prove the convergence under some given conditions.Research limitations/implicationsThe new method has its convergence proved and a number of research examples presented. The method proved efficient but there remains many difficulties in this area. Further research is needed to see whether this method can be used for solving initial value problems.Originality/valueProduces another tool and furthers the development of ADM by introducing a method based on infinite products.