DINA, a digital analyzer for Laplace, poisson, diffusion, and wave equations

IN AN extremely large number of problems concerning the behavior of physical systems the associated equation consists of the Laplace equation $\Delta ^2 u = 0 \eqno{\hbox{(1)}}$ or one of its close relatives Poisson equation $\Delta ^2 u = \rho \eqno{\hbox{(2)}}$ Diffusion equation $\Delta ^2 u = \kappa {\delta u \over \delta t} \eqno{\hbox{(3)}}$ Wave equation $\Delta ^2 u = {1 \over v^2} {\delta ^2 u \over \delta t^2} \eqno{\hbox{(4)}}$ For a given problem, equations 1 through 4 are not definitive as they stand, but require the specification of boundary and initial conditions peculiar to the problem at hand.