Further expansion of the computational horizons for the Green’s function modification of the method of functional equations

A specific class of boundary-value problems is targeted for partial differential equations that simulate potential fields induced in thin-wall structures. Computational efficiency is explored for one of the approaches to these problems. It is based on a Green’s function modification of the classical method of functional equations proposed by professor Kupradze. The problems are stated in regions of irregular configuration. It is shown that the approach appears workable for a broad range of problems including inverse formulations, which are always extremely expensive computationally. As the key component of the approach, Green’s functions are analytically constructed for governing differential equations prior to the actual computer work. This maintains a solid background for fast and accurate solution of direct problems, and creates, consequently, a promising environment for attacking targeted inverse problems.