ABSTRACT
Numerous elliptic partial differential equations arise in engineering and science. Two of the more common ones are the Laplace equation and the Poisson equation, presented below for the generic dependent variable f(x, y):
(9.7) (9.8)
where F(x, y) is a known nonhomogeneous term. The Laplace equation applies to problems in mass diffusion, heat diffusion (i.e., conduction), neutron diffusion, electrostatics, inviscid incompressible fluid flow, etc. In fact, the Laplace equation governs the potential of many physical quantities where the rate of flow of a particular property is proportional to the gradient of a potential. The Poisson equation is simply the nonhomogeneous Laplace equation. The presence of the nonhomogeneous term F(x, y) can greatly
