Solution of general vector partial differential equations by multidimensional transform methods

The multi-functional transformation model for the description of physical systems has been introduced to the field of discrete simulation of continuous systems. The multi-functional transformation is applied to physical systems which are described by partial differential equations, typically for the time and space variables. It allows the solution of an initial-boundary-value problem to expand in terms of its eigenfunctions and associated functions. This expansion serves as the starting point for the development of efficient discrete algorithms that are suitable for computer implementation. The purpose of this article is to extend the presented physical model to singular initial-boundary-value problems.