Journal of Applied & Computational Mathematics

To the Efficiency of a Green's Function Modification of the Method of Functional Equations

Abstract

Yuri A Melnikov

Analysis of the computational potential is provided for a modification of one of the numerical approaches to the classical boundary integral equations method. The originally proposed name of the approach is the method of functional equations, but in nowadays it is also referred to as the fundamental solutions method. Undesired after effects of this name flip are pointed out. The modification, implemented in this study, requires computer-friendly representations for some relevant Green's function and significantly enhances the resolving potential of the method. This work focuses on the exploration of the computational applicability of this modification. Chosen for that boundaryvalue problems and stated on regions of irregular configuration for second order elliptic equations with discontinuous coefficients.