The aim of that contribution however is to approximate just a function. Some orthogonality conditions which are used to construct HDMR expansion of the function and a factorization scheme based on a perturbative expansion are main components of the approach. Here we develop an HDMR expansion for the solution of the partial differential equations with some compatible boundary conditions first. The approach tries to expand everything, differential equation, boundary conditions, and the unknown function to be solved, into HDMR expansions. To this end some nominal factors, fluctuation functions, and product approximants are defined and determined.
Some illustrative applications finalizes the presentation.
The approach to be presented here seems to be a powerful candidate for applications to many dimensional problems like Poisson equation in N-dimension.