K. D. Cole
The Green's Function Solution Equation (GFSE) is the systematic procedure from which temperature may be found from Green's functions. The GFSE is briefly stated here; complete derivations, discussion, and examples are given in many standard references, including Carslaw and Jaeger (1959), Cole et al. (2011, chapter 3), and Barton (1989).
The GFSE equation takes on different forms depending on the differential equation and the coordinate system. Several distinct forms of the GFSE and the associated temperature problem are given below.