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.