  Current digital computers are about to hit basic physical boundaries with
respect to integration density, clock frequencies, and particularly energy
consumption. This requires the application of new computing paradigms, such as
quantum and analog computing in the near future. Although neither quantum nor
analog computer are general purpose computers they will play an important role
as co-processors to offload certain classes of compute intensive tasks from
classic digital computers, thereby not only reducing run time but also and
foremost power consumption.
  In this work, we describe a random walk approach to the solution of certain
types of partial differential equations which is well suited for combinations
of digital and analog computers (hybrid computers). The experiments were
performed on an Analog Paradigm Model-1 analog computer attached to a digital
computer by means of a hybrid interface. At the end we give some estimates of
speedups and power consumption obtainable by using future analog computers on
chip.
